Suppose you have a continuous and differentiable function on a closed interval f

Question

Suppose you have a continuous and differentiable function on a closed interval from a to b. Which of the following statements must be true?

There must be at least one point c in the open interval from a to b such that the slope of the line tangent to the curve at c is horizontal. There must be one point c in the open interval from a to b such that f?(a) = f?(c) = f?(b). There is at least one point c such that the slope of the line tangent to the function at c is equal to the slope of the secant line through the function at a and b. None of these statments must be true.

Explanation / Answer

"There must be at least one point c in the open interval from a to b such that the slope of the line tangent to the curve at c is horizontal."

this statement is true....

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