If and , where ,…

MATHEMATICS · Multi correct · CBSE · Mathematics · Integrals · Integrals

Problem

f(x)=\begin{cases}e^x,&0\le x\le1\\2-e^{x-1},&1<x\le2\\x-e,&2<x\le3\end{cases}

and

g(x)=\int_0^x f(t)\,dt

, where

x\in[1,3]

, then (1)

g(x)

has a local maximum at

x=1+\log_e2

and a local minimum at

x=e

. (2)

f(x)

has a local maximum at

x=1

and a local minimum at

x=2

. (3)

g(x)

has no local minimum. (4)

f(x)

has no local maximum.