Find critical numbers of f(x)=x³−3x.
Show a complete solution and verify with a second representation.
Unit 08 · Core Pathway
Analytical Applications & Optimization
How do derivatives reveal increasing behavior, extrema, shape, and optimal decisions?
Khaemenes Academy · Calculus I
Core Practice
Analytical Applications & Optimization · Show reasoning, notation, intervals, units, and corrections.
Name
Date
Where is the graph concave up?
Show a complete solution and verify with a second representation.
Why are endpoints checked for absolute extrema?
Show a complete solution and verify with a second representation.
Find f''(x) for f(x)=x³−3x.
Show a complete solution and verify with a second representation.
Why are endpoints checked for absolute extrema?
Show a complete solution and verify with a second representation.
Find f''(x) for f(x)=x³−3x.
Show a complete solution and verify with a second representation.
State the Mean Value Theorem conclusion.
Show a complete solution and verify with a second representation.
Where is the same function increasing?
Show a complete solution and verify with a second representation.
State the Mean Value Theorem conclusion.
Show a complete solution and verify with a second representation.
Where is the same function increasing?
Show a complete solution and verify with a second representation.
Where is the graph concave up?
Show a complete solution and verify with a second representation.
Find critical numbers of f(x)=x³−3x.
Show a complete solution and verify with a second representation.
Where is the graph concave up?
Show a complete solution and verify with a second representation.
A rectangle has perimeter 20. Write area as a function of width w.
Show a complete solution and verify with a second representation.
Give the maximum area.
Show a complete solution and verify with a second representation.
What should the final answer report?
Show a complete solution and verify with a second representation.