Let f(x) and g(x) be differentiable for 0<=x<=1 such that f(0)=0 g(0)=6 .let there exists a real number c in (0 1) such that f'(c)=2g'(c) then the value of g(1) must be

Let f(x) and g(x) be differentiable functions such that f'(x)g(x)!=f(x)g'(x) for any real x. Show that between any two real solution of f(x)=0, there is at least one real solution of g(x)=0.

Let f(x) and g(x) be differentiable functions such that f(x)+ int_(0)^(x) g(t)dt= sin x(cos x- sin x) and (f'(x))^(2)+(g(x))^(2) = 1,"then" f(x) and g (x) respectively , can be

Let f(x)and g(x) be twice differentiable functions on [0,2] satisfying f''(x)=g''(x) , f'(1)=4 , g'(1)=6 , f(2)=3 and g(2)=9 . Then what is f(x)-g(x) at x=4 equal to ?

Let f(x)=|x| and g(x)=|x^(3)|, then f(x) and g(x) both are continuous at x=0 (b) f(x) and g(x) both are differentiable at x=0 (c) f(x) is differentiable but g(x) is not differentiable at x=0 (d) f(x) and g(x) both are not differentiable at x=0

If f(x) and g(x) are two differentiable functions, show that f(x)g(x) is also differentiable such that (d)/(dx)[f(x)g(x)]=f(x)(d)/(dx){g(x)}+g(x)(d)/(dx){f(x)}

If both f(x) and g(x) are non-differentiable at x=a then f(x)+g(x) may be differentiable at x=a

Let f and g be differentiable on R and suppose f(0)=g(0) and f'(x) =0. Then show that f(x) =0

If f(x) and g(f) are two differentiable functions and g(x)!=0, then show trht (f(x))/(g(x)) is also differentiable (d)/(dx){(f(x))/(g(x))}=(g(x)(d)/(pi){f(x)}-g(x)(d)/(x){g(x)})/([g(x)]^(2))