Distance between local maximum and local minimum
up vote
2
down vote
favorite
If $P (x)$ be a polynomial of degree $3$ satisfying $P (-1)=10,P (1)=-6$ and $P(x)$ has maximum at $x=-1$ and $P'(x)$ has minima at $x=1$.Find the distance between the local maximum and local minimum of the curve.
euclidean-geometry maxima-minima
edited Nov 20 '16 at 12:33
naveen dankal
4,52321348
asked Nov 20 '16 at 12:08
user366398
365311
add a comment |
up vote
2
down vote
favorite
If $P (x)$ be a polynomial of degree $3$ satisfying $P (-1)=10,P (1)=-6$ and $P(x)$ has maximum at $x=-1$ and $P'(x)$ has minima at $x=1$.Find the distance between the local maximum and local minimum of the curve.
euclidean-geometry maxima-minima
edited Nov 20 '16 at 12:33
naveen dankal
4,52321348
asked Nov 20 '16 at 12:08
user366398
365311
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
If $P (x)$ be a polynomial of degree $3$ satisfying $P (-1)=10,P (1)=-6$ and $P(x)$ has maximum at $x=-1$ and $P'(x)$ has minima at $x=1$.Find the distance between the local maximum and local minimum of the curve.
euclidean-geometry maxima-minima
edited Nov 20 '16 at 12:33
naveen dankal
4,52321348
asked Nov 20 '16 at 12:08
user366398
365311
If $P (x)$ be a polynomial of degree $3$ satisfying $P (-1)=10,P (1)=-6$ and $P(x)$ has maximum at $x=-1$ and $P'(x)$ has minima at $x=1$.Find the distance between the local maximum and local minimum of the curve.
euclidean-geometry maxima-minima
euclidean-geometry maxima-minima
edited Nov 20 '16 at 12:33
naveen dankal
4,52321348
asked Nov 20 '16 at 12:08
user366398
365311
edited Nov 20 '16 at 12:33
naveen dankal
4,52321348
asked Nov 20 '16 at 12:08
user366398
365311
edited Nov 20 '16 at 12:33
naveen dankal
4,52321348
edited Nov 20 '16 at 12:33
naveen dankal
4,52321348
edited Nov 20 '16 at 12:33
naveen dankal
4,52321348
4,52321348
asked Nov 20 '16 at 12:08
user366398
365311
asked Nov 20 '16 at 12:08
user366398
365311
asked Nov 20 '16 at 12:08
user366398
365311
365311
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
2
down vote
accepted
Let the polynomial be $P(X)= ax^3+bx^2+cx+d$.
As per the given conditions we have :
$P(-1) = -a+b-c+d=10$
$P(1) = a+b+c+d=-6$
Also, $P'(-1)=3a-2b+c=0$
And $P"(1) = 6a+2b=0$
Solving for a,b,c,d gives
$P(X)=x^3-3x^2-9x+5$
=> $P'(X)=3x^2-6x-9=3(x+1)(x-3)$
This implies $x=-1$ is the point of maximum and $x=3$ is the point of minimum
Hence, the distance between $(-1,10)$ and $(3,-22)$ is $4sqrt{65}$
answered Nov 20 '16 at 12:17
naveen dankal
4,52321348
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
Let the polynomial be $P(X)= ax^3+bx^2+cx+d$.
As per the given conditions we have :
$P(-1) = -a+b-c+d=10$
$P(1) = a+b+c+d=-6$
Also, $P'(-1)=3a-2b+c=0$
And $P"(1) = 6a+2b=0$
Solving for a,b,c,d gives
$P(X)=x^3-3x^2-9x+5$
=> $P'(X)=3x^2-6x-9=3(x+1)(x-3)$
This implies $x=-1$ is the point of maximum and $x=3$ is the point of minimum
Hence, the distance between $(-1,10)$ and $(3,-22)$ is $4sqrt{65}$
answered Nov 20 '16 at 12:17
naveen dankal
4,52321348
add a comment |
up vote
2
down vote
accepted
Let the polynomial be $P(X)= ax^3+bx^2+cx+d$.
As per the given conditions we have :
$P(-1) = -a+b-c+d=10$
$P(1) = a+b+c+d=-6$
Also, $P'(-1)=3a-2b+c=0$
And $P"(1) = 6a+2b=0$
Solving for a,b,c,d gives
$P(X)=x^3-3x^2-9x+5$
=> $P'(X)=3x^2-6x-9=3(x+1)(x-3)$
This implies $x=-1$ is the point of maximum and $x=3$ is the point of minimum
Hence, the distance between $(-1,10)$ and $(3,-22)$ is $4sqrt{65}$
answered Nov 20 '16 at 12:17
naveen dankal
4,52321348
add a comment |
up vote
2
down vote
accepted
up vote
2
down vote
accepted
Let the polynomial be $P(X)= ax^3+bx^2+cx+d$.
As per the given conditions we have :
$P(-1) = -a+b-c+d=10$
$P(1) = a+b+c+d=-6$
Also, $P'(-1)=3a-2b+c=0$
And $P"(1) = 6a+2b=0$
Solving for a,b,c,d gives
$P(X)=x^3-3x^2-9x+5$
=> $P'(X)=3x^2-6x-9=3(x+1)(x-3)$
This implies $x=-1$ is the point of maximum and $x=3$ is the point of minimum
Hence, the distance between $(-1,10)$ and $(3,-22)$ is $4sqrt{65}$
answered Nov 20 '16 at 12:17
naveen dankal
4,52321348
Let the polynomial be $P(X)= ax^3+bx^2+cx+d$.
As per the given conditions we have :
$P(-1) = -a+b-c+d=10$
$P(1) = a+b+c+d=-6$
Also, $P'(-1)=3a-2b+c=0$
And $P"(1) = 6a+2b=0$
Solving for a,b,c,d gives
$P(X)=x^3-3x^2-9x+5$
=> $P'(X)=3x^2-6x-9=3(x+1)(x-3)$
This implies $x=-1$ is the point of maximum and $x=3$ is the point of minimum
Hence, the distance between $(-1,10)$ and $(3,-22)$ is $4sqrt{65}$
answered Nov 20 '16 at 12:17
naveen dankal
4,52321348
edited Nov 20 '16 at 12:29
answered Nov 20 '16 at 12:17
naveen dankal
4,52321348
answered Nov 20 '16 at 12:17
naveen dankal
4,52321348
answered Nov 20 '16 at 12:17
naveen dankal
4,52321348
4,52321348
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2022520%2fdistance-between-local-maximum-and-local-minimum%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
