Upper level Math class
Related-Rate Equation What is a related-rate equation?
Using Related Rates In Exercises $3-6,$ assume that $x$ and $y$ are both differentiable functions of $t$ and find the required values of $d y / d t$ and $d x / d x$ .
$y=\sqrt{x}$ (a) $\frac{d y}{d t}$ when $x=4$ $\frac{d x}{d t}=3$
(b)$$\frac{d x}{d t}$ when $x=25$$ $$\frac{d y}{d t}=2$$
$$x y=4$$$$\begin{array}{ll}{\text { (a) } \frac{d y}{d t} \text { when } x=8} & {\frac{d x}{d t}=10} \\ {\text { (b) } \frac{d x}{d t} \text { when } x=1} & {\frac{d y}{d t}=-6}\end{array}$$
Moving Point In Exercises $7-10,$ a point is moving along the graph of the given function at the rate $d x / d t .$ Find $d y / d t$ for the given values of $x .$
$$\begin{array}{l}{y=2 x^{2}+1 ; \frac{d x}{d t}=2 \text { centimeters per second }} \\ {(a) x=-1 \quad \text { (b) } x=0 \quad \text { (c) } x=1}\end{array}$$
$$\begin{array}{l}{y=\tan x ; \frac{d x}{d t}=3 \text { feet per second }} \\ {\text { (a) } x=-\frac{\pi}{3} \quad \text { (b) } x=-\frac{\pi}{4} \quad \text { (c) } x=0}\end{array}$$
Area The radius $r$ of a circle is increasing at a rate of 4 centimeters per minute. Find the rates of change of the area when $r=37$ centimeters.
