Connecting a Function, Its First Derivative, and its Second Derivative
Study Guide Overview
This study guide covers the graphical relationship between a function (f), its first derivative (f'), and its second derivative (f''). It explains how to determine a function's increasing/decreasing behavior, concavity, extrema (maxima/minima), and points of inflection by analyzing the graphs of f, f', and f''. The guide also includes practice problems and solutions to reinforce these concepts.
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Question 1 of 11
If the graph of is positive on an interval, what can be concluded about the graph of on that same interval? đ
f(x) is decreasing
f(x) is increasing
f(x) is concave down
f(x) has a relative minimum