If maximum value of $f(x) = 2x^3 + 3x^2 - 6ax + 10$ occurs at $x = -3$, then the value of $a$ is _____.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6 **
Given function:
$f(x)=2x^{3}+3x^{2}-6ax+10$
Maximum occurs at $x=-3$.
At a maximum, $f'(x)=0$.
Compute derivative:
$f'(x)=6x^{2}+6x-6a$
Set $f'(-3)=0$:
$6(-3)^{2}+6(-3)-6a=0$
$6(9)-18-6a=0$
$54-18-6a=0$
$36-6a=0$
$6a=36$
$a=6$
Answer: 6