APPLICATIONS OF DIFFERENTIATION
Derivative at a Value, Slope at a Value, Tangent Lines, Normal Lines, Points of Horizontal Tangents, Rolle's Theorem, Mean Value Theorem, Intervals of Increase and Decrease, Intervals of Concavity, Relative Extrema, Absolute Extrema, Optimization, Curve Sketching, Comparing a Function and its Derivatives, Motion Along a Line, Related Rates, Differentials, Newton's Method, Limits in Form of Definition of Derivative, L'Hôpital's Rule
All of our 136 video lessons are numbered below within their corresponding section. Select the section title to be brought to a compilation video lesson of that section. All of these videos are linked to our YouTube Channel. Enjoy!
Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The area of the spill increases at a rate of 9π m^2/min. How fast is the radius of the spill increasing when the radius is 10 m?
A conical paper cup is 10 cm tall with a radius of 10 cm. The cup is being filled with water so that the water level rises at a rate of 2 cm/sec. At what rate is water being poured into the cup when the water level is 8 cm?
A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the scenario can be modeled with right triangles. At what rate is the length of the person's shadow changing when the person is 16 ft from the lamppost?
An observer stands 700 ft away from a launch pad to observe a rocket launch. The rocket blasts off and maintains a velocity of 900 ft/sec. Assume the scenario can be modeled as a right triangle. How fast is the observer to rocket distance changing when the rocket is 2400 ft from the ground?