Answer:
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)
