Let `f(x)` and `g(x)` are two differentiable functions. If `f(x)=g(x)`, then show that `f'(x)=g'(x)`.
Is the converse true ? Justify your answer

Does there exist a differentiable function f(x) such that f(0) = -1, f(2) = 4 and f'(x)le2 for all x. Justify your answer.

Let f(x)=x^(2) and g(x)=2x+1 be two real functions. Find (f+g) (x), (f-g) (x), (fg) (x), (f/g) (x) .

f(x)=(1+x) g(x)=(2x-1) Show that fo(g(x))=go(f(x))

Let f(x)a n dg(x) be two differentiable functions in Ra n df(2)=8,g(2)=0,f(4)=10 ,a n dg(4)=8. Then prove that g^(prime)(x)=4f^(prime)(x) for at least one x in (2,4)dot

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

Is the function f(x) = |x| differentiable at the origin. Justify your answer.

Let f(x)a n dg(x) be differentiable functions such that f^(prime)(x)g(x)!=f(x)g^(prime)(x) for any real xdot 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)=x^(3)+x+1 and let g(x) be its inverse function then equation of the tangent to y=g(x) at x = 3 is

Let f(x)a n dg(x) be two continuous functions defined from RvecR , such that f(x_1)>f(x_2)a n dg(x_1) f(g(3alpha-4))