#Mark the correct alternative in each of the following The minimum value of the function f(x) = 2x 3 – 21x 2 + 36x – 20 is

Question

Philoid · Accepted Answer

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).