Question

The function f(x) = 2x³ – 15x² + 36x + 4 is maximum at x =

A. 3 

B. 0 

C. 4 

D. 2

Answer 1

Option : (D)

f(x) = 2x³ – 15x² + 36x + 4 

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

f’(x)= 6x² - 30x + 36 

= 6(x - 2)(x - 3) 

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

f’’(x) = 12x – 30 

For maxima at x = c, 

f’(c) = 0 and f’’(c) < 0 

f’(x) = 0 

⇒ x = 2 or x = 3 

f’’(2) = - 6 < 0 and f’’(3) = 6>0

Hence x = 2 is a point of maxima.