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

Verified by Experts

The correct Answer is:

C

Similar Questions

Explore conceptually related problems

If f(x)={:{(x", for " 0 le x lt 1),(2", for " x=1),(x+1", for " 1 lt x le 2):} , then f is

If f(x)={((1)/(e^(1/x)+1),",","when" x != 0),(0,",","when"x = 0):} , then

The function f(x)={{:(,(e^(1/x)-1)/(e^(1/x)+1),x ne 0),(,0,x=0):}

If f(x)=(x+1)/((x-2)(x-5)) , then in [0, 1]

IF f(x)=x,-1lexle1 , then function f(x) is

If f(x) ={((5^(x)-e^(x))/(sin 2x),",",x != 0),(1/2(log 5+1),",",x = 0):} , then

If {:(f(x),=((e^(kx)-1)^(2)sinx)/(x^(3)),",",x != 0),(,=4, ",",x = 0):} is continuous at x = 0, then k =

If f(x) = {((x^(2)-4x+3)/(x^(2)-1), ",","for"x != 1),(2, ",", "for"x = 1 ):} , then

If f: R to R be defined by f(x)={(2x:xgt3),(x^(2):1lt x le 3),(3x:x le 1):} Then, f(-1)+f(2)+f(4) is