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Question: The function f(x)=\(\int_{- 1}^{x}{t(e^{t} - 1)(t - 1)(t - 2)^{3}}\) (t–3)<sup>5</sup>dt has a local...

The function f(x)=∫−1xt(et−1)(t−1)(t−2)3\int_{- 1}^{x}{t(e^{t} - 1)(t - 1)(t - 2)^{3}} (t–3)5dt has a local maximum at x =

A

0

B

1

C

2

D

3

Answer

2

Explanation

Solution

f(x) = ∫–1x+(et–1)(t–1)(t–2)3(t–3)5dt\int_{–1}^{x}{+ (e^{t}–1)(t–1)(t–2)^{3}(t–3)^{5}}dt

f ' (x) = x (ex – 1) (x – 1) (x – 2)3 (x – 3)5

f ' (x) + ve its – ve at x = 2

Hence x = 2 is maxima pt