f(x) = {=0.8(x-2.5)² +1.5, if a < 2.5 -x+4, ifa > 2.5 Use at least 3 decimal places if you need to round. (a). Use the formula for f(x) to compute the largest acceptable value for x that guarantees f(x) will be within 0.3 of 1.5. Imax (b). Use the formula for f(x) to compute the smallest possible value for that guarantees f(x) will be within 0.3 of 1.5. I min (c). Use the formula for f(x) to compute the largest input tolerance, d, that guarantees f(x) will be within 0.3 of 1.5. (Enter dne if no such d exists.) 8 = 2 M stv MacBook Pro AC
f(x) = {=0.8(x-2.5)² +1.5, if a < 2.5 -x+4, ifa > 2.5 Use at least 3 decimal places if you need to round. (a). Use the formula for f(x) to compute the largest acceptable value for x that guarantees f(x) will be within 0.3 of 1.5. Imax (b). Use the formula for f(x) to compute the smallest possible value for that guarantees f(x) will be within 0.3 of 1.5. I min (c). Use the formula for f(x) to compute the largest input tolerance, d, that guarantees f(x) will be within 0.3 of 1.5. (Enter dne if no such d exists.) 8 = 2 M stv MacBook Pro AC
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![### Function Definition and Analysis Task
Consider the function \( f(x) \) defined as follows:
\[
f(x) =
\begin{cases}
-0.8(x - 2.5)^2 + 1.5, & \text{if } x < 2.5 \\
x + 4, & \text{if } x \geq 2.5
\end{cases}
\]
### Instruction for Analysis
Use at least 3 decimal places if you need to round.
**(a)** Use the formula for \( f(x) \) to compute the largest acceptable value for \( x \) that guarantees \( f(x) \) will be within 0.3 of 1.5.
\[ x_{\text{max}} = \boxed{} \]
**(b)** Use the formula for \( f(x) \) to compute the smallest possible value for \( x \) that guarantees \( f(x) \) will be within 0.3 of 1.5.
\[ x_{\text{min}} = \boxed{} \]
**(c)** Use the formula for \( f(x) \) to compute the largest input tolerance, \( \delta \), that guarantees \( f(x) \) will be within 0.3 of 1.5.
(Enter \(\text{dne}\) if no such \(\delta\) exists.)
\[ \delta = \boxed{} \]
### Graph Description
The graph displays \( f(x) \) with two distinct segments:
1. **Quadratic Segment**: On the left for \( x < 2.5 \), showing a downward opening parabola centered at \( x = 2.5 \).
2. **Linear Segment**: On the right for \( x \geq 2.5 \), showing a straight line with a positive slope intersecting at \( y = 4 \).
The transition between these segments occurs at \( x = 2.5 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe1b1d143-3544-4565-ae01-c2b2100e15ce%2F40c00565-6dc6-4195-ba0f-c03c986a8cd2%2Ftgtm21o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Function Definition and Analysis Task
Consider the function \( f(x) \) defined as follows:
\[
f(x) =
\begin{cases}
-0.8(x - 2.5)^2 + 1.5, & \text{if } x < 2.5 \\
x + 4, & \text{if } x \geq 2.5
\end{cases}
\]
### Instruction for Analysis
Use at least 3 decimal places if you need to round.
**(a)** Use the formula for \( f(x) \) to compute the largest acceptable value for \( x \) that guarantees \( f(x) \) will be within 0.3 of 1.5.
\[ x_{\text{max}} = \boxed{} \]
**(b)** Use the formula for \( f(x) \) to compute the smallest possible value for \( x \) that guarantees \( f(x) \) will be within 0.3 of 1.5.
\[ x_{\text{min}} = \boxed{} \]
**(c)** Use the formula for \( f(x) \) to compute the largest input tolerance, \( \delta \), that guarantees \( f(x) \) will be within 0.3 of 1.5.
(Enter \(\text{dne}\) if no such \(\delta\) exists.)
\[ \delta = \boxed{} \]
### Graph Description
The graph displays \( f(x) \) with two distinct segments:
1. **Quadratic Segment**: On the left for \( x < 2.5 \), showing a downward opening parabola centered at \( x = 2.5 \).
2. **Linear Segment**: On the right for \( x \geq 2.5 \), showing a straight line with a positive slope intersecting at \( y = 4 \).
The transition between these segments occurs at \( x = 2.5 \).
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