## Precalculus (6th Edition) Blitzer

$100 \pi$ cubic inches per inch
a) Now, $f′(x)=\lim_\limits{ h\to 0} \dfrac{f(x+h)-f(x)}{h}$ or, $=\lim_\limits{ h\to 0} \dfrac{\dfrac{4 \pi}{3}(x+h)^3-\dfrac{4 \pi}{3}x^3}{h}$ or, $=\lim_\limits{ h\to 0} \dfrac{\dfrac{4 \pi}{3}(x^3+3x^2h+3xh^2+h^3)-\dfrac{4 \pi}{3}x^3}{h}$ or, $=\lim_\limits{ h\to 0} \dfrac{(4 \pi x^2+4\pi xh+(4/3) \pi h^2}{h}$ or, $=4 \pi x^2$ and $f(5)=4 \pi (5)^2=100 \pi$