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Calculus finds best values because a smooth curve is flat at its peaks and valleys. Those flat spots are where the derivative is zero.
- Name what you want to maximize or minimize.
- Use the constraint to get one variable.
- Differentiate and set it to 0.
- Check that it really is the best.
Work through it
A rectangle has perimeter 40. What's its largest possible area?
Use the constraint., so
Write the area.
Set the derivative to 0., so
Calculate., a square
Find the minimum of .
Differentiate.
Set to 0.
Evaluate.
Watch out for this
Stopping at when the question asks for the area.
Read back what was asked and substitute.
The short version
Write one quantity in terms of one variable. Set its derivative to 0. Check the ends and confirm it's the best.
Write one quantity in terms of one variable. Set its derivative to 0. Check the ends and confirm it's the best.
Your turn
Prefer paper? Print the More derivatives and applications worksheet, with an answer key.
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