Applications of Derivatives
Use derivatives for tangent lines, maxima and minima, optimization and related rates, with the setup and the first- and second-derivative tests shown. Try “maximize the area of a rectangle with perimeter 40”.
Try an example:
How the Applications of Derivatives works
- Write the quantity to optimize as a function of one variable, using the constraint.
- Set the derivative to zero and solve for critical points.
- Confirm a maximum or minimum with the second derivative test and answer in context.
Frequently asked questions
How do I find a tangent line?
Find the derivative at the point for the slope, then use y − y₁ = m(x − x₁).
How do I know it is a maximum?
If f″ is negative at the critical point it is a maximum; if positive, a minimum.
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