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The document discusses the Mean Value Theorem (MVT) and provides two examples of using it to find the value of c for given functions f(x) and g(x). Specifically, it shows applying the MVT to find c for the functions f(x)=x^2 on the interval [1,2] and g(x)=sin(x) on the interval [0,pi].

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If f(x) is continuous for all a<=x<=b and f(x) is
differentiable for all a<x<b, then there must exist at least
one number c, a<c<b, such that f '(c) = (f(b)f(a))/(ba)

25

303

Find c, 1<c<2, for f(x)=x^2 satisfying the MVT.

26

303

Find c such that 0<c<pi for g(x)=sin(x) satisfying the MVT.

27

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25. 303 If f(x) is continuous for all a<=x<=b and f(x) is differentiable for all a<x<b, then there must exist at least one number c, a<c<b, such that f '(c) = (f(b)f(a))/(ba) 25

26. 303 Find c, 1<c<2, for f(x)=x^2 satisfying the MVT. 26

27. 303 Find c such that 0<c<pi for g(x)=sin(x) satisfying the MVT. 27

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