Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$? [on hold]Find point closest to the given pointClosest point in $y = sqrtx$ to the origin is at $x=-1/2$?Find the point on graph of $xy=12$ that is closest to the point $(5,0)$Optimization, point on parabola closest to another pointWhat is the closest point on the graph of $x^2-y^2=4$ to the point $(0,1)$?Finding the points on a curve, closest to a specific pointThe point on $y = sqrtln x$ closest to $(4,0)$nth closest point with integer coordinates to a given pointFind the points on the graph of the function that are closest to the given point.Which point of the graph of $y=sqrtx$ is closest to the point $(1,0)$?
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Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$? [on hold]
Find point closest to the given pointClosest point in $y = sqrtx$ to the origin is at $x=-1/2$?Find the point on graph of $xy=12$ that is closest to the point $(5,0)$Optimization, point on parabola closest to another pointWhat is the closest point on the graph of $x^2-y^2=4$ to the point $(0,1)$?Finding the points on a curve, closest to a specific pointThe point on $y = sqrtln x$ closest to $(4,0)$nth closest point with integer coordinates to a given pointFind the points on the graph of the function that are closest to the given point.Which point of the graph of $y=sqrtx$ is closest to the point $(1,0)$?
$begingroup$
Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$ ?
calculus optimization
edited 23 hours ago
user21820
40.1k544162
asked yesterday
Julian CallegariJulian Callegari
81
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Julian Callegari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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put on hold as off-topic by Shailesh, Leucippus, user21820, John Omielan, B. Goddard 20 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Shailesh, Leucippus, user21820, John Omielan, B. Goddard
add a comment |
$begingroup$
Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$ ?
calculus optimization
edited 23 hours ago
user21820
40.1k544162
asked yesterday
Julian CallegariJulian Callegari
81
New contributor
Julian Callegari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
put on hold as off-topic by Shailesh, Leucippus, user21820, John Omielan, B. Goddard 20 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Shailesh, Leucippus, user21820, John Omielan, B. Goddard
add a comment |
$begingroup$
Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$ ?
calculus optimization
edited 23 hours ago
user21820
40.1k544162
asked yesterday
Julian CallegariJulian Callegari
81
New contributor
Julian Callegari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$ ?
calculus optimization
calculus optimization
edited 23 hours ago
user21820
40.1k544162
asked yesterday
Julian CallegariJulian Callegari
81
New contributor
Julian Callegari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 23 hours ago
user21820
40.1k544162
asked yesterday
Julian CallegariJulian Callegari
81
New contributor
Julian Callegari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 23 hours ago
user21820
40.1k544162
edited 23 hours ago
user21820
40.1k544162
edited 23 hours ago
user21820
40.1k544162
40.1k544162
asked yesterday
Julian CallegariJulian Callegari
81
New contributor
Julian Callegari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Julian CallegariJulian Callegari
81
asked yesterday
Julian CallegariJulian Callegari
81
81
New contributor
Julian Callegari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Julian Callegari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Julian Callegari is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Shailesh, Leucippus, user21820, John Omielan, B. Goddard 20 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Shailesh, Leucippus, user21820, John Omielan, B. Goddard
put on hold as off-topic by Shailesh, Leucippus, user21820, John Omielan, B. Goddard 20 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Shailesh, Leucippus, user21820, John Omielan, B. Goddard
add a comment |
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2 Answers
2
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oldest
votes
$begingroup$
HINT
If a point is on the specified graph, it looks like $p_x = left(x,7-x^2right)$. So the square $D$ of the distance $d$ of $p_x$ to $(0,4)$ is given by
$$
D(x) = d^2(x) = (x-0)^2 + (7-x^2-4)^2
$$
Can you simplify and minimize $D(x)$?
answered yesterday
gt6989bgt6989b
35.6k22557
$endgroup$
add a comment |
$begingroup$
Take a point $P(a,7-a^2)$ of the parabola. The slope between this point and $Q(0,4)$ is
$frac7-a^2-4a$ while the derivate of $y$ at $a$ is $-2a$. Now the line through $PQ$ must hit the parabola at a right angle, hence
$$frac7-a^2-4adot(-2a)=-1,$$
from where $a$ is easily calculated.
answered 22 hours ago
Michael HoppeMichael Hoppe
11.3k31837
$endgroup$
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
HINT
If a point is on the specified graph, it looks like $p_x = left(x,7-x^2right)$. So the square $D$ of the distance $d$ of $p_x$ to $(0,4)$ is given by
$$
D(x) = d^2(x) = (x-0)^2 + (7-x^2-4)^2
$$
Can you simplify and minimize $D(x)$?
answered yesterday
gt6989bgt6989b
35.6k22557
$endgroup$
add a comment |
$begingroup$
HINT
If a point is on the specified graph, it looks like $p_x = left(x,7-x^2right)$. So the square $D$ of the distance $d$ of $p_x$ to $(0,4)$ is given by
$$
D(x) = d^2(x) = (x-0)^2 + (7-x^2-4)^2
$$
Can you simplify and minimize $D(x)$?
answered yesterday
gt6989bgt6989b
35.6k22557
$endgroup$
add a comment |
$begingroup$
HINT
If a point is on the specified graph, it looks like $p_x = left(x,7-x^2right)$. So the square $D$ of the distance $d$ of $p_x$ to $(0,4)$ is given by
$$
D(x) = d^2(x) = (x-0)^2 + (7-x^2-4)^2
$$
Can you simplify and minimize $D(x)$?
answered yesterday
gt6989bgt6989b
35.6k22557
$endgroup$
HINT
If a point is on the specified graph, it looks like $p_x = left(x,7-x^2right)$. So the square $D$ of the distance $d$ of $p_x$ to $(0,4)$ is given by
$$
D(x) = d^2(x) = (x-0)^2 + (7-x^2-4)^2
$$
Can you simplify and minimize $D(x)$?
answered yesterday
gt6989bgt6989b
35.6k22557
answered yesterday
gt6989bgt6989b
35.6k22557
answered yesterday
gt6989bgt6989b
35.6k22557
answered yesterday
gt6989bgt6989b
35.6k22557
35.6k22557
add a comment |
add a comment |
$begingroup$
Take a point $P(a,7-a^2)$ of the parabola. The slope between this point and $Q(0,4)$ is
$frac7-a^2-4a$ while the derivate of $y$ at $a$ is $-2a$. Now the line through $PQ$ must hit the parabola at a right angle, hence
$$frac7-a^2-4adot(-2a)=-1,$$
from where $a$ is easily calculated.
answered 22 hours ago
Michael HoppeMichael Hoppe
11.3k31837
$endgroup$
add a comment |
$begingroup$
Take a point $P(a,7-a^2)$ of the parabola. The slope between this point and $Q(0,4)$ is
$frac7-a^2-4a$ while the derivate of $y$ at $a$ is $-2a$. Now the line through $PQ$ must hit the parabola at a right angle, hence
$$frac7-a^2-4adot(-2a)=-1,$$
from where $a$ is easily calculated.
answered 22 hours ago
Michael HoppeMichael Hoppe
11.3k31837
$endgroup$
add a comment |
$begingroup$
Take a point $P(a,7-a^2)$ of the parabola. The slope between this point and $Q(0,4)$ is
$frac7-a^2-4a$ while the derivate of $y$ at $a$ is $-2a$. Now the line through $PQ$ must hit the parabola at a right angle, hence
$$frac7-a^2-4adot(-2a)=-1,$$
from where $a$ is easily calculated.
answered 22 hours ago
Michael HoppeMichael Hoppe
11.3k31837
$endgroup$
Take a point $P(a,7-a^2)$ of the parabola. The slope between this point and $Q(0,4)$ is
$frac7-a^2-4a$ while the derivate of $y$ at $a$ is $-2a$. Now the line through $PQ$ must hit the parabola at a right angle, hence
$$frac7-a^2-4adot(-2a)=-1,$$
from where $a$ is easily calculated.
answered 22 hours ago
Michael HoppeMichael Hoppe
11.3k31837
edited 21 hours ago
answered 22 hours ago
Michael HoppeMichael Hoppe
11.3k31837
answered 22 hours ago
Michael HoppeMichael Hoppe
11.3k31837
answered 22 hours ago
Michael HoppeMichael Hoppe
11.3k31837
11.3k31837
add a comment |
add a comment |
