Q. 275.0( 1 Vote )

# #Mark the correct alternative in each of the following

Let f(x) = 2x^{3} – 3x^{2} – 12x + 5 on [–2, 4]. The relative maximum occurs at x =

A. –2

B. –1

C. 2

D. 4

Answer :

f(x) = 2x^{3} – 3x^{2} – 12x + 5, x∈[-2,4]

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

f’(x)= 6x^{2} – 6x – 12=6(x+1)(x-2)

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

f’’(x)=12x-6

For maxima at x=c, f’(c)=0 and f’’(c)<0

f’(x)=0 ⇒ x=-1 or 2

f’’(-1)=-18<0 and f’’(2)=18>0

Hence, x=-1 is the point of local maxima.

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