뒤로College Algebra Unit 2 Review – Step-by-Step Study Guidance
스터디 가이드 - 스마트 노트
자료에 맞춘 맞춤형 노트, 핵심 정의, 예시, 맥락을 확장해 제공합니다.
Q9. Use the graph of the given function to find any relative maxima and relative minima. f(x) = x^3 - 3x^2 + 1
Background
Topic: Relative Extrema of Functions
This question tests your ability to interpret a graph to identify relative maxima and minima (also called local maximum and minimum points). These are points where the function changes direction from increasing to decreasing (maximum) or from decreasing to increasing (minimum).
Key Terms and Concepts:
Relative Maximum: The highest point in a particular section of a graph.
Relative Minimum: The lowest point in a particular section of a graph.
To find these points, look for where the graph changes direction.
Step-by-Step Guidance
Examine the graph and identify where the function changes from increasing to decreasing (for a maximum) and from decreasing to increasing (for a minimum).
Locate the x-values where these changes occur. These are typically at the peaks (maximum) and valleys (minimum) of the graph.
Read the corresponding y-values at these x-values to determine the actual maximum and minimum values.
Check if there are any other points on the graph where the function changes direction.
Try solving on your own before revealing the answer!
Final Answer:
The function has a relative maximum at x = 0, with a maximum value of 1, and a relative minimum at x = 2, with a minimum value of -3.
These points are found by observing where the graph changes direction: at x = 0 (peak) and x = 2 (valley).
