Let `f(x)=(x-1)(x-2)(x-3)` then prove that there is more than one 'c' in (1,3) such that `f'(c )=0`

Let f(x ) = (x - 1)(x - 2)(x -3). Prove that there is more than one ‘c’ in (1,3) such that f ’(c) = 0

Let f(x) and g(x) be differentiable functions for 0 le x le 1 such that f(0) = 2, g(0) = 0, f(1) = 6 . Let there exist a real number c in (0,1) such that f ’(c) = 2 g ’(c), then g(1) =

Suppose f(x) = x(x+3)(x-2), x in [-1, 4] . Then a value of c in (-1, 4) satisfying f'(c ) = 10 is

Suppose f(x)=x(x+3)(x-2),x in [-1,4] . Then a value of c in (-1,4) satisfying f' ( c) = 10 is .

If f(x)= 2x^2+3x+5 , then prove that f'(0)+3f'(-1)=0

Let Q(x)=f(x)+f(1-x) and f''(x)lt0 for 0ltxlt1 then on (0,1/2)