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` (c)`f` is decreasing in the neighbourhood of `a` if `g(a)>0` (d)`f` is decreasing in the neighbourhood of `a` if `g(a)<0`

If f(x)=3x+1,g(x)=x^3+2 , then (f+g)/(fg) (0) =?

If f(x)=x+1,g(x)=x^2+1 , then (f+g)/(fg) (0) =?

Statement 1: The function f(x)=x In x is increasing in (1/e ,oo) Statement 2: If both f(x)a n dg(x) are increasing in (a , b),t h e nf(x)g(x) must be increasing in (a,b).

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

If f(x)=(x+1)/(x-1)a n dg(x)=1/(x-2),t h e n discuss the continuity of f(x),g(x),a n dfog(x)dot

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.

If f(x)=(e^(x))/(g(x)),g(0)=6,g'(0)=2 , then f'(0) is

If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e n(d u)/(d v) is

If f(x)=e^xg(2x),g(0)=4 and g'(0) = 2 then f'(0) is equal to

Let g(x)=f(x)+f(1-x) and f''(x)>0AAx in (0,1)dot Find the intervals of increase and of g(x)dot