Let f ( x )= x 3-4 x 2-16 x +64. If ∫ limitsα4 f ( x ) dx is maximum, where α

Question

Let f ( x )= x 3-4 x 2-16 x +64. If ∫ limitsα4 f ( x ) dx is maximum, where α<0, then α is equal to (A) -4 (B) -16 (C) -32 (D) none of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/d528beff4b7593538a11af76d68bd80d-.png" /> f(x)=x2(x-4)-16(x-4) =(x2-16)(x-4) =(x-4)2(x+4) For ∫ limitsα4 f(x) d x to be maximum, α must be -4 .

Q. Let $f (x) = x^{3} - 4 x^{2} - 16 x + 64$ . If $α \int 4 f (x) d x$ is maximum, where $α < 0$ , then $α$ is equal to

$- 4$

-16

-32

none of these

$f (x) = x^{2} (x - 4) - 16 (x - 4)$
$= (x^{2} - 16) (x - 4)$
$= (x - 4)^{2} (x + 4)$
For $α \int 4 f (x) d x$ to be maximum, $α$ must be -4 .

Q. Let f(x)=x3−4x2−16x+64. If α∫4​f(x)dx is maximum, where α<0, then α is equal to

−4

-16

-32

none of these

f(x)=x2(x−4)−16(x−4) =(x2−16)(x−4) =(x−4)2(x+4) For α∫4​f(x)dx to be maximum, α must be -4 .

Q. Let $f (x) = x^{3} - 4 x^{2} - 16 x + 64$ . If $α \int 4 f (x) d x$ is maximum, where $α < 0$ , then $α$ is equal to

$- 4$

$f (x) = x^{2} (x - 4) - 16 (x - 4)$
$= (x^{2} - 16) (x - 4)$
$= (x - 4)^{2} (x + 4)$
For $α \int 4 f (x) d x$ to be maximum, $α$ must be -4 .