Question #308088

Question 6 [2]


State the mean Value Theorem.

1
Expert's answer
2022-03-10T18:13:41-0500

The theorem states that if ff is a continuous function on the closed interval [a,b][a,b] and differentiable on the open interval (a,b),(a,b), then there exists a point cc in (a,b)(a,b) such that the tangent at cc is parallel to the secant line through the endpoints (a,f(a)){\displaystyle {\big (}a,f(a){\big )}} and (b,f(b)),{\displaystyle {\big (}b,f(b){\big )}}, that is,


f(c)=f(b)f(a)ba.{\displaystyle f'(c)={\frac {f(b)-f(a)}{b-a}}.}


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