Critical points, extrema and increasing intervalsFind the critical points of a cubic, classify them as local maxima or minima, and find where the function is increasing or decreasing.Position, velocity and accelerationDifferentiate a position function to find velocity and acceleration, and find when the object is at rest.Optimization problemsWrite a function for the quantity to maximize, using a constraint to reduce it to one variable, and find its maximum with the derivative.Related ratesDifferentiate a formula with respect to time to relate the rates at which two quantities change, for growing circles, squares and spheres.Concavity and inflection pointsFind the second derivative of a cubic or quartic, its inflection points, and the intervals where the function is concave up or concave down.
Calculus Applications of derivatives Worksheets
Critical points and local extrema, increasing and decreasing intervals, concavity and inflection points, velocity and acceleration, optimization and related rates. Every sheet comes with a computed answer key.
Make a mixed applications of derivatives sheet