Related Rates Examples

Let $y = 2(x^2 - 3x)$

a. Find $\frac{dy}{dt}$ when $x = 3$ given $\frac{dx}{dt} = 2$

b. Find $\frac{dx}{dt}$ when $x = 1$ given $\frac{dy}{dt} = 5$

A 10 by 6 foot rectangular swimming pool is being filled. Find the rate at which the height of the water rises if the hose is pouring at $20 \frac{{ft}^3}{hour}$

Find the rate of change of the height of the water level if the hose is pouring $2 \frac{{ft}^3}{m}$

A man is walking away from a lamp at $5 \frac{ft}{s}$

a. Find the rate at which the tip of his shadow is changing

b. Find the rate at which the length of his shadow is changing