Question

The least value of the function f(x) = x³ – 18x² + 96x in the interval [0, 9] is :

A. 126 

B. 135 

C 160 

D. 0

Answer 1

Option : (D)

f(x) = x³ - 18x² + 96x 

f(x) = 3x² - 36x + 96 

f’(x) = 0 

3x² - 36x + 96 = 0 

x² - 12x + 32 = 0 

x² - 8x - 4x + 32 = 0 

x (x - 8) - 4(x - 8) = 0 

Now we have 

f(0) = 0,

f(4) = 160,

f(9) = 135 

Hence in the given interval least value is f(0) = 0