## Calculus 10th Edition

(a) F'(4) = 50 vibrations/sec/lb (b) F'(9) = $\frac{100}{3}$ or 33 $\frac{1}{3}$ vibrations/sec/lb
F = 200$\sqrt T$ F(t) = 200$T^{\frac{1}{2}}$ F'(t) = 200($\frac{1}{2})T^{-\frac{1}{2}}$ F'(t) = $\frac{100}{\sqrt T}$ (a) When T = 4: F'(4) = $\frac{100}{\sqrt 4}$ F'(4) = $\frac{100}{2}$ F'(4) = 50 vibrations/sec/lb (b) When T = 9: F'(4) = $\frac{100}{\sqrt 9}$ F'(4) = $\frac{100}{3}$ vibrations/sec/lb