If maximum value of $f(x) = 2x^3 + 3x^2 - 6ax + 10$ occurs at $x = -3$, then the value of $a$ is _____.

6

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