If `f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt x le 2,, and g(x) = int_(0)^(x) f(t ) dt","),( x- e,,"," 2lt x le 3 ,, ""):}`
` x in [ 1, 3 ] `, then
a. g(x) has local maxima at `x=1+log_(e)2` and local minima at x=e
b. f(x) has local maxima at x=1 and local minima at x=2
c. g(x) has no local minima
d. f(x) has no local maxima

Options

A. g(x) has local maxima at `x=1+log_(e)2` and local minima at x=e
B. f(x) has local maxima at x=1 and local minima at x=2
C. g(x) has no local minima
D. f(x) has no local maxima

Answer

A, B