Find critical numbers of f(x)=x³−3x.
Generalize, analyze an edge case, or defend the result without relying on technology.
Unit 08 · Extended Pathway
Analytical Applications & Optimization
How do derivatives reveal increasing behavior, extrema, shape, and optimal decisions?
Khaemenes Academy · Calculus I
Extended Practice
Analytical Applications & Optimization · Show reasoning, notation, intervals, units, and corrections.
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Date
State the Mean Value Theorem conclusion.
Generalize, analyze an edge case, or defend the result without relying on technology.
Where is the same function increasing?
Generalize, analyze an edge case, or defend the result without relying on technology.
Why are endpoints checked for absolute extrema?
Generalize, analyze an edge case, or defend the result without relying on technology.
Where is the graph concave up?
Generalize, analyze an edge case, or defend the result without relying on technology.
Where is the same function increasing?
Generalize, analyze an edge case, or defend the result without relying on technology.
State the Mean Value Theorem conclusion.
Generalize, analyze an edge case, or defend the result without relying on technology.
Find f''(x) for f(x)=x³−3x.
Generalize, analyze an edge case, or defend the result without relying on technology.
Find critical numbers of f(x)=x³−3x.
Generalize, analyze an edge case, or defend the result without relying on technology.
State the Mean Value Theorem conclusion.
Generalize, analyze an edge case, or defend the result without relying on technology.
Find the width that maximizes that area.
Generalize, analyze an edge case, or defend the result without relying on technology.
What should the final answer report?
Generalize, analyze an edge case, or defend the result without relying on technology.