Prepared : Wed Oct 20 20:59:16 CDT 1999

MATH 1271

QUIZ III

1) Given

find dy/dx.

Use the Chain Rule for the outer parantheses:

Now to find the derivative of we will have to use Chain Rule once more:

So the final answer will be

2) The area of a circle is decreasing at the rate of . At what rate is the radius of the circle decreasing when its area is ?

The area of a circle is given by the formula

where r is the radius of the circle.

In the problem we are given the rate of change of area, which is the derivative of the area with respect to time. So differentiate A with respect to time by using the chain rule.

We know what dA/dt is. To be able to find dr/dt all we need is r, when A=75 .

So r= . Plugging this into the previous equation we find

hence