Correct Answer - Option 3 : 36

__Concept:__

Following steps to **finding maxima and minima** using derivatives.

- Find the derivative of the function.
- Set the derivative equal to 0 and solve. This gives the values of the maximum and minimum points.
- Now we have to find the second derivative.

- f``(x) is less than 0 then the given function is said to be maxima
- If f``(x) Is greater than 0 then the function is said to be minima

__Calculation:__

Let f(x) = x^{3} - 12x^{2} + kx – 8

Differentiating with respect to x, we get

⇒ f’(x) = 3x^{2} – 24x + k

It is given that function attains its maximum value of the interval [0, 3] at x = 2

∴ f’(2) = 0

⇒ 3 × 2^{2} – (24 × 2) + k = 0

∴ k = 36