Question

Let f(x) = e-* VX E[-1, 1) then​

Answer 1

Answer:

ANSWER

f(x)=xe

x(x−1)

⇒f

′

(x)=e

x(1−x)

+x

2

(−1)e

x(1−x)

+x(1−x)e

x(1−x)

=−e

x(1−x)

(2x

2

−x−1)=−e

x(1−x)

(x−1)(x+1/2)

f

′

(x)=0 at x=−1/2,1 and f

′

(x)>0 when −1/2<x<1

⇒f(x) is increasing function on [−1/2,1]

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