Let and define

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let f(x)={ax+2,x<26,x>2f(x)=\begin{cases}ax+2,& x<2\\6,& x>2\end{cases} and define F(x)=10+∫1xf(t) dtF(x)=10+\int_{1}^{x} f(t)\,dt. Determine the value of aa for which FF is differentiable at x=2x=2.

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