1. Assume that x and y are both differentiable functions of t and find the required values of d...

Question:

1. Assume that x and y are both differentiable functions of t and find the required values of {eq}\frac{\mathrm{d} y}{\mathrm{d} t} {/eq} and {eq}\frac{\mathrm{d} x}{\mathrm{d} t} {/eq}.

(a) Find {eq}\frac{\mathrm{d} y}{\mathrm{d} t} {/eq} when x = 5, given that {eq}\frac{\mathrm{d} x}{\mathrm{d} t} {/eq} = 5.

(b) Find {eq}\frac{\mathrm{d} x}{\mathrm{d} t} {/eq} when x = 6, given that {eq}\frac{\mathrm{d} y}{\mathrm{d} t} {/eq} = 1.

2. A spherical balloon is inflated with gas at a rate of 700 cubic centimeters per minute.

(a) How fast is the radius of the balloon changing at the instant the radius is 60 centimeters?

(b) How fast is the radius of the balloon changing at the instant the radius is 80 centimeters?

Rate of Change:

We will find the rate of change of radius by first writing the expression for the volume of the sphere and then differentiating it and then plug-in the values.

Answer and Explanation: 1

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To find the rate of change of radius we will use the volume expression of the sphere:

{eq}V=\frac{4}{3}\pi r^{3} {/eq}

Now let us differentiate the...

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Rate of Change vs. Negative Rate of Change

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Chapter 8 / Lesson 7
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Rates of change show how fast a parameter changes with respect to another reference parameter. Learn about rates of change, how to graph rates of change, and see the difference between positive and negative rates of change.


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