Think About It Describe the relationship betweenthe rate of change of y and the rate of change of x ineach expression. Assume all variables and derivativesare positive. (a) $\frac{d y}{d t}=3 \frac{d x}{d t}$(b) $\frac{d y}{d t}=x(L-x) \frac{d x}{d t}, \quad 0 \leq x \leq L$

Think About It Describe the relationship betweenthe rate of change of y and the rate of change of x ineach expression. Assume all variables and derivativesare positive. (a) $\frac{d y}{d t}=3 \frac{d x}{d t}$(b) $\frac{d y}{d t}=x(L-x) \frac{d x}{d t}, \quad 0 \leq x \leq L$

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 29E: Changing Water Levels The graph shows the depth of water W in a reservoir over a one-year period as...

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

Think About It Describe the relationship between
the rate of change of y and the rate of change of x in
each expression. Assume all variables and derivatives
are positive.

(a) $\frac{d y}{d t}=3 \frac{d x}{d t}$
(b) $\frac{d y}{d t}=x(L-x) \frac{d x}{d t}, \quad 0 \leq x \leq L$

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