Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$? [on hold]Find point closest to the...
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Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$? [on hold]
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$begingroup$
Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$ ?
calculus optimization
edited 19 hours ago
user21820
40.1k544162
asked 23 hours ago
Julian CallegariJulian Callegari
81
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put on hold as off-topic by Shailesh, Leucippus, user21820, John Omielan, B. Goddard 16 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
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$begingroup$
Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$ ?
calculus optimization
edited 19 hours ago
user21820
40.1k544162
asked 23 hours ago
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 16 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
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Which point on the graph of $ y=7-x^2$ is closest to the point $(0,4)$ ?
calculus optimization
edited 19 hours ago
user21820
40.1k544162
asked 23 hours ago
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 19 hours ago
user21820
40.1k544162
asked 23 hours ago
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 19 hours ago
user21820
40.1k544162
asked 23 hours ago
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 19 hours ago
user21820
40.1k544162
edited 19 hours ago
user21820
40.1k544162
edited 19 hours ago
user21820
40.1k544162
40.1k544162
asked 23 hours ago
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 23 hours ago
Julian CallegariJulian Callegari
81
asked 23 hours ago
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 16 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
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Shailesh, Leucippus, user21820, John Omielan, B. Goddard 16 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
If this question can be reworded to fit the rules in the help center, please edit the question.
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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 23 hours ago
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
$frac{7-a^2-4}{a}$ while the derivate of $y$ at $a$ is $-2a$. Now the line through $PQ$ must hit the parabola at a right angle, hence
$$frac{7-a^2-4}{a}dot(-2a)=-1,$$
from where $a$ is easily calculated.
answered 18 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 23 hours ago
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 23 hours ago
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 23 hours ago
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 23 hours ago
gt6989bgt6989b
35.6k22557
answered 23 hours ago
gt6989bgt6989b
35.6k22557
answered 23 hours ago
gt6989bgt6989b
35.6k22557
answered 23 hours ago
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
$frac{7-a^2-4}{a}$ while the derivate of $y$ at $a$ is $-2a$. Now the line through $PQ$ must hit the parabola at a right angle, hence
$$frac{7-a^2-4}{a}dot(-2a)=-1,$$
from where $a$ is easily calculated.
answered 18 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
$frac{7-a^2-4}{a}$ while the derivate of $y$ at $a$ is $-2a$. Now the line through $PQ$ must hit the parabola at a right angle, hence
$$frac{7-a^2-4}{a}dot(-2a)=-1,$$
from where $a$ is easily calculated.
answered 18 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
$frac{7-a^2-4}{a}$ while the derivate of $y$ at $a$ is $-2a$. Now the line through $PQ$ must hit the parabola at a right angle, hence
$$frac{7-a^2-4}{a}dot(-2a)=-1,$$
from where $a$ is easily calculated.
answered 18 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
$frac{7-a^2-4}{a}$ while the derivate of $y$ at $a$ is $-2a$. Now the line through $PQ$ must hit the parabola at a right angle, hence
$$frac{7-a^2-4}{a}dot(-2a)=-1,$$
from where $a$ is easily calculated.
answered 18 hours ago
Michael HoppeMichael Hoppe
11.3k31837
edited 16 hours ago
answered 18 hours ago
Michael HoppeMichael Hoppe
11.3k31837
answered 18 hours ago
Michael HoppeMichael Hoppe
11.3k31837
answered 18 hours ago
Michael HoppeMichael Hoppe
11.3k31837
11.3k31837
add a comment |
add a comment |
