Q29 of 137 Page 19

#Mark the correct alternative in each of the following

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


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).

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