What is the answer to this question? explain why and show your work !

The maximum value of f(x) is 4.

Step-by-step explanation:

We have to find maximum value of f(x) = 2x³ - 9x² + 12x - 1 (1) on [-1,2].

Now, differentiating equation (1) with respect to x, we get

f'(x) = 6x² - 18x + 12 = 0 {Condition for maxima is f'(x) = 0}

⇒ x² - 3x + 2 = 0

⇒ (x - 1)(x - 2) = 0

⇒ x =1 or x = 2

Now, both the values lies in the interval [-1,2]

But, f(1) = 2 - 9 + 12 - 1 = 4

and f(2) = 2(8) - 9(4) + 12(2) - 1 = 16 - 36 + 24 - 1 = 3

Therefore, maximum value of f(x) is 4. (Answer)