Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.7 - Derivatives and Rates of Change - 2.7 Exercises: 46

Answer

The rate of change of the temperature after an hour is $-\frac{5}{6}^oF/min$, or the turkey loses $\frac{5}{6}^oF$ every minute after an hour.

Work Step by Step

We would call the function from the graph $T=f(t)$ To estimaate the slope of the tangent at $t=60$, we would - pick 2 close points from $t=60$, which are $t=30$ and $t=90$ and figure out the values of $f(30)$ and $f(90)$ - Find the value of $\frac{f(90)-f(30)}{90-30}$. The result is the estimated slope of the tangent. From the graph, we see that $f(30)=150$ and $f(90)=100$ Therefore, the slope of the tangent is $$m=\frac{f(90)-f(30)}{90-30}=\frac{100-150}{60}=-\frac{5}{6}$$ The unit here is $^oF/min$. In conclusion, the rate of change of the temperature after an hour is $-\frac{5}{6}^oF/min$, or the turkey loses $\frac{5}{6}^oF$ every minute after an hour.
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