If `f^(prime)x=g(x)(x-a)^2,w h e r eg(a)!=0,a n dg` is continuous at `x=a ,` then `f` is increasing in the neighbourhood of `a` if `g(a)>0` `f` is increasing in the neighbourhood of `a` if `g(a)<0` `f` is decreasing in the neighbourhood of `a` if `g(a)>0` `f` is decreasing in the neighbourhood of `a` if `g(a)<0`

If f^(prime)(x)=g(x)(x-a)^2,w h e r eg(a)!=0,a n dg is continuous at x=a , then (a) f is increasing in the neighbourhood of a if g(a)>0 (b) f is increasing in the neighbourhood of a if g(a) 0 (d) f is decreasing in the neighbourhood of a if g(a)<0

If f^(prime)(x)=g(x)(x-a)^2,w h e r eg(a)!=0,a n dg is continuous at x=a , then (a) f is increasing in the neighbourhood of a if g(a)>0 (b) f is increasing in the neighbourhood of a if g(a) 0 (d) f is decreasing in the neighbourhood of a if g(a)<0

Given that f(x) = xg (x)//|x| g(0) = g'(0)=0 and f(x) is continuous at x=0 then the value of f'(0)

If f(x)=(x) and g(x)=(5x-2) Find f0g and g0f

If f(x)=e^(x)g(x),g(0)=2,g'(0)=1, then f'(0) is

If f(x)=e^(x)g(x),g(0)=2,g'(0)=1, then f'(0) is

If f"(x)>0 for all x in R, f'(3)=0,and g(x)=f(tan^2 x-2tan x+4),0

Which of the following statement is always true? (a)If f(x) is increasing, the f^(-1)(x) is decreasing. (b)If f(x) is increasing, then 1/(f(x)) is also increasing. (c)If fa n dg are positive functions and f is increasing and g is decreasing, then f/g is a decreasing function. (d)If fa n dg are positive functions and f is decreasing and g is increasing, the f/g is a decreasing function.

Which of the following statement is always true? (a)If f(x) is increasing, the f^(-1)(x) is decreasing. (b)If f(x) is increasing, then 1/(f(x)) is also increasing. (c)If fa n dg are positive functions and f is increasing and g is decreasing, then f/g is a decreasing function. (d)If fa n dg are positive functions and f is decreasing and g is increasing, the f/g is a decreasing function.