Question

Let f(x) = 2x³ – 3x² – 12x + 5 on [–2, 4]. The relative maximum occurs at x = 

A. –2 

B. –1 

C. 2 

D. 4

Answer 1

Option : (B)

f(x) = 2x³ – 3x² – 12x + 5, x ∈ [-2,4] 

Differentiating f(x) with respect to x, we get 

f’(x) = 6x2 – 6x – 12 

= 6(x + 1)(x - 2) 

Differentiating f’(x) with respect to x, we get 

f’’(x) = 12x - 6 

For maxima at x = c, 

f’(c) = 0 and f’’(c) < 0

 f’(x) = 0 

⇒ x = -1 or 2

f’’(-1) = -18 < 0 and 

f’’(2) = 18 > 0

Hence, 

x = -1 is the point of local maxima.