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If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,,...

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

has no local minima

D

has no local maxima

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The correct Answer is:
A, B
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