Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Only question 9. I would like to compare my answer
![**Problem 9:**
Consider the piecewise function \( f(x) \) defined by
\[
f(x) =
\begin{cases}
x^2 + ax - b & \text{if } x \geq 2 \\
3x - b & \text{if } x < 2
\end{cases}
\]
Which of the following values for \( a \) and \( b \) make the function differentiable at \( x = 2 \)?
- (a) \( b = 8 - 2a \) for any value for \( a \).
- (b) \( a = 7 \) and any value for \( b \).
- (c) There are no values of \( a \) and \( b \) that make the function differentiable.
- (d) \( a = 7 \) and \( b = -6 \).
- (e) \( a = 3 \) and \( b = -2 \).
---
**Problem 10:**
The function \( M(t) \) gives the depth (in meters) of the Athabasca Glacier as a function of the temperature \( t \) that the atmosphere has warmed above the 1951–1980 average global surface air temperature (in °C). As of 2011, the Athabasca Glacier was losing an average of 5 meters of depth per year. (Source: CBC News, NASA)
Which of the following best describes \( M'(3) \)?
- (a) \( M'(3) \) is the average rate that the glacier is melting (in meters/year) when the average global surface air temperature increases by 3°C per year.
- (b) \( M'(3) \) is the rate of cooling of the average global surface air temperature (in °C/ meter) when the depth of the Athabasca Glacier decreases by 17 meters.
- (c) \( M'(3) \) is the rate of change of the depth of the Athabasca Glacier (in meters/°C).](https://content.bartleby.com/qna-images/question/9d5280c1-0888-4121-94fb-2a368f5b3705/35a3c154-750a-47f2-b19f-0775728aa5e2/z26ygu.jpeg)
Transcribed Image Text:**Problem 9:**
Consider the piecewise function \( f(x) \) defined by
\[
f(x) =
\begin{cases}
x^2 + ax - b & \text{if } x \geq 2 \\
3x - b & \text{if } x < 2
\end{cases}
\]
Which of the following values for \( a \) and \( b \) make the function differentiable at \( x = 2 \)?
- (a) \( b = 8 - 2a \) for any value for \( a \).
- (b) \( a = 7 \) and any value for \( b \).
- (c) There are no values of \( a \) and \( b \) that make the function differentiable.
- (d) \( a = 7 \) and \( b = -6 \).
- (e) \( a = 3 \) and \( b = -2 \).
---
**Problem 10:**
The function \( M(t) \) gives the depth (in meters) of the Athabasca Glacier as a function of the temperature \( t \) that the atmosphere has warmed above the 1951–1980 average global surface air temperature (in °C). As of 2011, the Athabasca Glacier was losing an average of 5 meters of depth per year. (Source: CBC News, NASA)
Which of the following best describes \( M'(3) \)?
- (a) \( M'(3) \) is the average rate that the glacier is melting (in meters/year) when the average global surface air temperature increases by 3°C per year.
- (b) \( M'(3) \) is the rate of cooling of the average global surface air temperature (in °C/ meter) when the depth of the Athabasca Glacier decreases by 17 meters.
- (c) \( M'(3) \) is the rate of change of the depth of the Athabasca Glacier (in meters/°C).
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