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Question: The value of the function f(x) = \(\int _ { - 1 } ^ { \mathrm { x } } \mathrm { t } \left( \mathrm...

The value of the function

f(x) = ∫−1xt(et−1)(t−1)(t−2)3(t−3)5dt\int _ { - 1 } ^ { \mathrm { x } } \mathrm { t } \left( \mathrm { e } ^ { \mathrm { t } } - 1 \right) ( \mathrm { t } - 1 ) ( \mathrm { t } - 2 ) ^ { 3 } ( \mathrm { t } - 3 ) ^ { 5 } \mathrm { dt } is minimum at –

A

x = 0

B

x = 1

C

x = 2

D

) x = 1 and x = 3

Explanation

Solution

)

Sol. f ¢(x) = x.(ex –1) (x – 1) (x – 2)3 (x – 5)5 = 0

Ž x = 0, 1, 2, 3,

Min. at x = 1, 3