Answer
(a) F'(4) = 50 vibrations/sec/lb
(b) F'(9) = $\frac{100}{3}$ or 33 $\frac{1}{3}$ vibrations/sec/lb
Work Step by Step
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
