Prove that the curves `y=f(x),[f(x)>0],a n dy=f(x)sinx ,w h e r ef(x)` is differentiable function, have common tangents at common points.

Prove that the curves y_(1) = f (x) (f(x) gt 0) and y_(2) = f(x) sin x, where f(x) is a differentiable function, are tangent to each other at the common points.

f(x)=int_0^x e^t f(t)dt+e^x , f(x) is a differentiable function on x in R then f(x)=

If f(x+y)=f(x)dotf(y),\ AAx in R\ a n df(x) is a differentiability function everywhere. Find f(x) .

If f is a differentiable function and 2f(sinx) + f(cosx)=x AA x in R then f'(x)=

f(x+y)=f(x).f(y)AA x,y in R and f(x) is a differentiable function and f'(0)=1,f(x)!=0 for any x.Findf(x)

At an extreme point of a function f(X) the tangent to the curve is

Let f(x+y)=f(x)+f(y)+2xy-1 for all real x and f(x) be a differentiable function.If f'(0)=cosalpha, the prove that f(x)>0AA x in R

Prove that the function If f(x)={:{((x)/(1+e^(1//x)) ", " x ne 0),(" "0", " x=0):} is not differentiable