Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 48CR
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![### Evaluating Piecewise Functions
Given the function \( f(x) \) defined as:
\[ f(x) =
\begin{cases}
x^3 - 4x^2 & \text{if } x \leq -4 \\
2x^2 & \text{if } -4 < x < 4 \\
x^3 - 48 & \text{if } x \geq 4
\end{cases}
\]
We are to evaluate \( f(x) \) at \( x = -4 \), \( x = 2 \), and \( x = 4 \).
---
### Evaluation Steps:
1. **Evaluate \( f(-4) \)**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- A. \( f(-4) = \) \( \boxed{\text{(Simplify your answer.)}} \)
- B. The answer is undefined.
2. **Evaluate \( f(2) \)**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- A. \( f(2) = \) \( \boxed{\text{(Simplify your answer.)}} \)
- B. The answer is undefined.
3. **Evaluate \( f(4) \)**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- A. \( f(4) = \) \( \boxed{\text{(Simplify your answer.)}} \)
- B. The answer is undefined.
---
### Explanation of Piecewise Function
- For \( x \leq -4 \), use \( f(x) = x^3 - 4x^2 \).
- For \( -4 < x < 4 \), use \( f(x) = 2x^2 \).
- For \( x \geq 4 \), use \( f(x) = x^3 - 48 \).
Make sure to follow these rules when plugging in the values for \( x \) to determine \( f(x) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F375a8daa-a061-40df-aa13-f324a3b06fab%2F265eb48d-aa13-4a6e-8fbc-28b1ce4b8246%2Fyqe2pv6_processed.png&w=3840&q=75)
Transcribed Image Text:### Evaluating Piecewise Functions
Given the function \( f(x) \) defined as:
\[ f(x) =
\begin{cases}
x^3 - 4x^2 & \text{if } x \leq -4 \\
2x^2 & \text{if } -4 < x < 4 \\
x^3 - 48 & \text{if } x \geq 4
\end{cases}
\]
We are to evaluate \( f(x) \) at \( x = -4 \), \( x = 2 \), and \( x = 4 \).
---
### Evaluation Steps:
1. **Evaluate \( f(-4) \)**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- A. \( f(-4) = \) \( \boxed{\text{(Simplify your answer.)}} \)
- B. The answer is undefined.
2. **Evaluate \( f(2) \)**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- A. \( f(2) = \) \( \boxed{\text{(Simplify your answer.)}} \)
- B. The answer is undefined.
3. **Evaluate \( f(4) \)**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- A. \( f(4) = \) \( \boxed{\text{(Simplify your answer.)}} \)
- B. The answer is undefined.
---
### Explanation of Piecewise Function
- For \( x \leq -4 \), use \( f(x) = x^3 - 4x^2 \).
- For \( -4 < x < 4 \), use \( f(x) = 2x^2 \).
- For \( x \geq 4 \), use \( f(x) = x^3 - 48 \).
Make sure to follow these rules when plugging in the values for \( x \) to determine \( f(x) \).
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