The area (in cm ) of a square whose side length increases from cm to cm is given by…

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

Problem

The area AA (in cm2^2) of a square whose side length increases from 55 cm to (5+h)(5+h) cm is given by A(h)=(5+h)2−25h,  h≠0.A(h)=\dfrac{(5+h)^2-25}{h},\; h\neq 0. Calculate the instantaneous rate of change of the area with respect to the side length at the instant when the side length is exactly 55 cm. Interpret your answer in appropriate units.

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