If `f(x)=x^(2)-6x+8` and there exists a point c in the interval `[2,4]` such that `f'(c)=0`, then what is the value of c?

Does there exist a point c(in)(0,pi/2) such that f' (c)= 0 where f(x) = sin 2x ?

Let f(x) and g(x) be differentiable for 0<=x<=2 such that f(0)=2,g(0)=1, and f(2)=8. Let there exist a real number c in [0,2] such that f'(c)=3g'(c). Then find the value of g(2)

Let f(x) and g(x) be differentiable for 0 le x le 2 such that f(0) = 2, g(0) = 1, and f(2) = 8. Let there exist a real number c in [0, 2] such that f'(c) = 3g'(c) . Then find the value of g(2).

Let f(x) and g(x) be differentiable for 0 le x le 1 such that f(0)=0, g(0)=0, f(1)=6 . Let there exist a real number c in (0, 1) such that f'(c )=2g'(c ) , then the value of g(1) must be :

Function f is defined by f(x)=(3)/(2)x+c . If f(6)=1 , what is the value of f(c) ?

The graph of f(x)=x^2 and g(x)=cx^3 intersect at two points, If the area of the region over the interval [0,1/c] is equal to 2/3 , then the value of (1/c+1/(c^2)) is

If "f(x)= x^3-6x^2+12x+50" ,then the maximum value of "f" is attained in the interval "[-2,2]" at the point "

Let the function f be defined such that f(x)=x^(2)- c, where c is constant. If f(-2)=6 , what is the value of c?