Classifying Critical Points and Extreme Values for a Function
Key Questions
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Here is how to find and classify a critical point of
f .Remember that
x=c is called a critical value off iff'(c)=0 orf'(c) is undefined.f'(x)=3x^2=0 Rightarrow x=0 is a critical number.(Note:
f' is defined everywhere,0 is the only critical value.)Observing that
f'(x)=3x^2 ge 0 for allx ,f' does not change sign around the critical value0 .Hence,
f(0) is neither a local maximum nor a local minimum by First Derivative Test.
Questions
Graphing with the First Derivative
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Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)
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Identifying Stationary Points (Critical Points) for a Function
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Identifying Turning Points (Local Extrema) for a Function
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Classifying Critical Points and Extreme Values for a Function
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Mean Value Theorem for Continuous Functions