# ap calculus ab free response application of derivatives

Polynomial Functions 5m 4s. Trigonometric Functions 6m 45s. Inverse Trigonometric Functions 5m 58s. Trigonometric Identities 17m 42s.

Exponential Functions 5m 53s. Logarithmic Functions 7m 8s. Rational Functions 15m 36s. Conic Sections 14m 58s. Section 2: Limits and Continuity. Solving Limits with Algebra 8m 1s. Rational Limit Rules 3m 16s. One Sided Limits 9m 57s. Special Trigonometric Limits 8m 28s. Limits: Multiple Choice Practice 6m 16s. Section 3: Derivatives. Basic Rules of Differentiation 7m 7s.

Power Rule 7m 14s. Trigonometric Rules 7m 53s. Product Rule 11m 11s. Quotient Rule 16m 50s. Chain Rule 19m 48s. Higher Order Derivatives 15m. Derivatives of Exponential Functions 13m 14s.

Derivatives of Logarithmic Functions 11m 30s. Derivatives of Inverse Trigonometric Functions 16m 54s. Implicit Differentiation 16m 53s.

Coding Bat. Google Drive. Contact Mr. Instructional Technology. Professional Development. Calculate Derivatives Determine higher order derivatives Interpret the meaning of a derivative within a problem Use derivatives to analyze properties of a function Solve problems involving optimization Apply the Mean Value Theorem to describe the behavior of a function over an interval.

Completed Notes Below. Quarter Assessment Review. Extreme Values of a Function Notesheet. Completed Notes. Extreme Values of a Function Practice. Possible Answers:. Correct answer:. Report an Error. Example Question 2 : Applications Of Derivatives.

Explanation : To determine the rate of change of the surface area of the spherical bubble, we must relate it to something we do know the rate of change of - the volume. Example Question 3 : Applications Of Derivatives. Explanation : To find the rate of change of the diameter, we must relate the diameter to something we do know the rate of change of: the surface area. Example Question 4 : Applications Of Derivatives. Explanation : To determine the rate of change of the circumference at a given radius, we must relate the circumference rate of change to the rate of change we know - that of the volume.

Example Question 5 : Applications Of Derivatives. Explanation : To determine the rate of the change of the angle opposite to the base of the given right triangle, we must relate it to the rate of change of the base of the triangle when the triangle is a certain area.

Example Question 1 : Applications Of Derivatives. The position of a car is given by the equation. Explanation : This is a related rates problem.

Recall that , where r is the radius. Since the radius is given as 1 unit, we can write this equation as. Plugging this information in, we get This is the answer. Example Question 8 : Applications Of Derivatives.

Simplifying the right side gives us Since and are variables, we will wait to plug values into them until after we take the derivative. Using implicit differentiation to find the derivative with respect to time, we get We only care about the instant that and. Since we are dealing with physical distances, we will only use the positive 8. Plugging all the information into our derivative equation gives us The negative makes sense, because the man is falling down, so the height is getting smaller.

Example Question 9 : Applications Of Derivatives. If the car starts out at a distance of 3 miles from its home, how far will it be after 4 hours? Graph Analysis. Notes and Key. First Derivative Test Notes. First Derivative Test Practice. Extreme Values of Functions Practice. Connecting Graphs WS. The 2nd Derivative, Concavity and Points of Inflection. AP Practice with Second Derivative. Curve Sketching 2 Days. Unit 1 - Limits and Continuity.

Unit 2 - Derivatives. Unit 3 - Applications of Derivatives.