Question

The minimum value of the function f(x) = 2x³ – 21x² + 36x – 20 is :

A. –128 

B. –126 

C. –120 

D. none of these

Answer 1

Option : (A)

f(x) = 2x³ – 21x² + 36x – 20 

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

f’(x)= 6x² - 42x + 36 

= 6(x - 1)(x - 6) 

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

f’’(x) = 12x - 42 

for minima at x = c, 

f’(c) = 0 and f’’(c) > 0 

f’(x) = 0 

⇒ x = 1 or x = 6 

f’’(1) = - 30 < 0 and 

f’’(6) = 30 > 0

Hence,

x = 6 is the point of minima for f(x) and f(6) = -128 is the local minimum value of f(x).