A differentiable function satisfies and .

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

Problem

A differentiable function hh satisfies h(5)=−1h(5)=-1 and h′(5)=4h'(5)=4. (1) Evaluate lim⁡x→5h(x)+1x−5\displaystyle \lim_{x\to 5} \frac{h(x)+1}{x-5}. Show how the given information about hh leads directly to the numerical value of the limit. (2) Determine lim⁡x→5h(x)\displaystyle \lim_{x\to 5} h(x). Explain your reasoning. (3) State whether hh is continuous at x=5x=5 and justify your conclusion using results from parts (a) and (b).

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