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.g is continuous at x = 0 , then f and g are separately continuous at x = 0 .

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

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.

Let f''(x) gt 0 AA x in R and g(x)=f(2-x)+f(4+x). Then g(x) is increasing in

If f''(x) gt forall in R, f(3)=0 and g(x) =f(tan^(2)x-2tanx+4y)0ltxlt(pi)/(2) ,then g(x) is increasing in

If f(x)=3x+1 and g(x)=x^(3)+2 then ((f+g)/(f*g))(0) is:

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

If f(x)=sgn(x)={(|x|)/(x),x!=0,0,x=0 and g(x)=f(f(x)) then at x=0,g(x) is