The function is considered on the interval

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

The function g(x)=sin⁡2xg(x)=\sin 2x is considered on the interval [0,π][0,\pi]. Work through the following tasks. (i) Determine the average rate of change of gg on [0,π][0,\pi]. (ii) Solve for all real numbers cc in (0,π)(0,\pi) that satisfy g′(c)g'(c) equal to the average rate calculated in part (i). (iii) State the total number of distinct values of cc obtained and provide a brief justification for your count.

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