If the function `f: [0, 16]-> R` is differentiable. If `0 < alpha < 1 and 1 < beta < 2` , then `int_0^16 f(t)dt` is equal to

If the function f : [0,8] to R is differentiable, then for 0 < alpha <1 < beta < 2 , int_0^8 f(t) dt is equal to

If the function f:[0,4]->R is differentiable, the show that for a , b , in (0,4),f^2(4) - f^2(0) =8f^(prime)(a)f(b)

If the function f defined on R-{0} is a differentiable function and f(x^3)=x^5 for all x, then f'(27)=

If the function f defined on R-{0} os a dIfferentiable function and f(x^3)=x^5 for all x, then f'(27)=

Let f be any continuously differentiable function on [a, b] and twice differentiable on (a, b) such that f(a)=f'(a)=0" and "f(b)=0 . Then-

A function f:R rarr R satisfies that equation f(x+y)=f(x)f(y) for all x,y in R ,f(x)!=0. suppose that the function f(x) is differentiable at x=0 and f'(0)=2. Prove that f'(x)=2f(x)

If f be a continuous function on [0,1] differentiable in (0,1) such that f(1)=0, then there exists some c in(0,1) such that

If an even function f is differentiable at x=0, then f '(0)=