27 1) Consider the function f(x) = - 16x, x = 0. a) Sketch the graph of y = f(x), for -4 ≤ x ≤ 3 and -50 ≤ y ≤ 100. b) i) Use your graphic display calculator to find the zero of f(x). ii) Use your graphic display calculator to find the coordinates of the local minimum point.
27 1) Consider the function f(x) = - 16x, x = 0. a) Sketch the graph of y = f(x), for -4 ≤ x ≤ 3 and -50 ≤ y ≤ 100. b) i) Use your graphic display calculator to find the zero of f(x). ii) Use your graphic display calculator to find the coordinates of the local minimum point.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Problem 1: Analyzing the Function**
Consider the function \( f(x) = \frac{27}{x^2} - 16x \), where \( x \neq 0 \).
### Part a
- **Task:** Sketch the graph of \( y = f(x) \) for the domain \( -4 \leq x \leq 3 \) and range \( -50 \leq y \leq 100 \).
### Part b
- **Tasks:**
1. Use your graphic display calculator to find the zero of \( f(x) \).
2. Use your graphic display calculator to find the coordinates of the local minimum point.
**Note:** Make sure to analyze the graph carefully to identify key features such as intercepts, asymptotes, and critical points.
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