If f(x)={ex,0≤x≤12−ex−1,1<x≤2x−e,2<x≤3f(x) = \begin{cases} e^x, & 0 \le x \le 1 \\ 2 - e^{x-1}, & 1 < x \le 2 \\ x - e, & 2 < x \le 3 \end{cases}…

Problem

If f(x)={ex,0≤x≤12−ex−1,1<x≤2x−e,2<x≤3f(x) = \begin{cases} e^x, & 0 \le x \le 1 \\ 2 - e^{x-1}, & 1 < x \le 2 \\ x - e, & 2 < x \le 3 \end{cases} and g(x)=∫0xf(t) dtg(x) = \int_0^x f(t)\,dt, x∈[1,3]x \in [1,3], then a. g(x)g(x) has local maxima at x=1+log⁡e2x = 1 + \log_e 2 and local minima at x=ex = e b. f(x)f(x) has local maxima at x=1x = 1 and local minima at x=2x = 2 c. g(x)g(x) has no local minima d. f(x)f(x) has no local maxima

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