Let be defined on the closed interval

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let g(x)=x3−5x+2g(x)=x^{3}-5x+2 be defined on the closed interval [−2,3][-2,3]. Explain why there must exist at least one number cc in (−2,3)(-2,3) such that g′(c)=2g'(c)=2.

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