Let `f(x)` be differentiable function and `g(x)` be twice differentiable function. Zeros of `f(x),g^(prime)(x)` be `a , b` , respectively, `(a

Let f(x) be differentiable function and g(x) be twice differentiable function. Zeros of f(x), g'(x) be a, b, respectively, (a lt b) . Show that there exists at least one root of equation f'(x) g'(x) + f(x) g''(x) = "0 on" (a, b) .

Let f(x) be differentiable function and g(x) be twice differentiable function.Zeros of f(x),g'(x) be a,b, respectively,(a

Let g(x) be the inverse of an invertible function f(x) which is differentiable at x=c . Then g^(prime)(f(x)) equal.

If y =f(u) is differentiable function of u, and u=g(x) is a differentiable function of x, then prove that y= f [g(x)] is a differentiable function of x and (dy)/(dx)=(dy)/(du)xx(du)/(dx) .

If both f(x)&g(x) are differentiable functions at x=x_(0) then the function defiend as h(x)=Maximum{f(x),g(x)}

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all x, then g'f(x) is equal to

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all x, then g''f(x) is equal to