Rolle’s Theorem and the Mean Value Theorem

For Rolle's theorem function must be continues on

For Rolle's theorem function must be differentiable on

Rolle's theorem tells about the

Does Rolle's theorem is applicable if f(a) is not the same as f(b)

Does Rolle's theorem is applicable

Does Rolle's theorem is applicable

The function, F, above satisfies the conclusion of Rolle's Theorem in the interval [a,b] because:

I. F is continuous

II. F is differentiable on (a,b)

III. F(a) = F(b) = 0

Which of the functions given below satisfy all three conditions of Rolle's theorem?a) f(x) = cos(x) , for x in [0 , 2π]

b) g(x) = |x - 2| , for x in [0 , 4]

c) h(x) = 1 / x² , for x in [-1 , 1]

$$Find\ the\ value\ of\ c\ for\ the\ function\ f\left(x\right)=x^{2\ }\ in\ \left[-1,1\right]$$  

Check that function f(x) = x ² - 4 x + 3 on the interval [1 , 3] satisfies all conditions of Rolle's theorem and then find all values of x = c such that f '(c) = 0.

The solution set to the equation: $$4^{x^2-4x}=2^{-6}$$  

For what value of x is the equation  $$2^{\left(2x+7\right)}\ =\ 2^{15}$$  true?

In the standard (x,y) coordinate plane, what is the slope of the line given by the equation 4x = 7y + 5 ?

What is the slope of the line through (−2,1) and (2,−5) in the standard (x,y) coordinate plane?

 Let the function f be defined as   $$5x^{2\ }-7\left(4x+3\right)$$ What is the value of f(3) ?