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If f(x)={{:(x",",0lexle1),(2-e^(x-1)",",...

If `f(x)={{:(x",",0lexle1),(2-e^(x-1)",",1ltxle2),(x-e",",2ltxle3):}` and `g'(x)=f(x), x in [1,3]`, then```

A

g(x) has a local maxima at `x=1+log_e2` and local minima at x=e

B

f(x) has a local maxima at x=1 and local minima at x=2

C

f(x) and g(x) have same points of local maxima and local minima

D

None of these

Text Solution

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The correct Answer is:
C
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