Find the absolute maximum and minimum, if either exists, for f(x) = x - 8x + 9. Find the first derivative of f. f'(x) = 2x – 8

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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### Problem Statement

Find the absolute maximum and minimum, if either exists, for \( f(x) = x^2 - 8x + 9 \).

### Solution

#### Step 1: Find the First Derivative of \( f \).

The first derivative of \( f(x) \) is calculated as follows:

\[ f'(x) = 2x - 8 \]

This derivative will help identify critical points and potential extrema of the function.
Transcribed Image Text:### Problem Statement Find the absolute maximum and minimum, if either exists, for \( f(x) = x^2 - 8x + 9 \). ### Solution #### Step 1: Find the First Derivative of \( f \). The first derivative of \( f(x) \) is calculated as follows: \[ f'(x) = 2x - 8 \] This derivative will help identify critical points and potential extrema of the function.
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