#Mark the correct alternative in each of the following The function f(x) = 2x 3 – 15x 2 + 36x + 4 is maximum at x =

Question

Philoid · Accepted Answer

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.