1 / 12

Objectives: Be able to find the derivative of an equation with respect to various variables.

Related Rates. Objectives: Be able to find the derivative of an equation with respect to various variables. Be able to solve various rates of change applications. Critical Vocabulary: Derivative, Rate of Change. I. Derivatives.

jefferson-tommy
Download Presentation

Objectives: Be able to find the derivative of an equation with respect to various variables.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Related Rates • Objectives: • Be able to find the derivative of an equation with respect to various variables. • Be able to solve various rates of change applications. Critical Vocabulary: Derivative, Rate of Change

  2. I. Derivatives Example 1: Find the derivative of y with respect to x: x2 + y2 = 25 Example 2: Find the derivative of x with respect to y: x2 + y2 = 25

  3. I. Derivatives Example 3: Find the derivative of y with respect to t: x2 + y2 = 25 Example 4: Find the derivative of x with respect to t: x2 + y2 = 25

  4. I. Derivatives Example 5: Find dy/dt when x = 2 of the equation 4xy = 12 given that dx/dt = 4 (If x = 2, Then y = 3/2)

  5. Related Rates • Objectives: • Be able to find the derivative of an equation with respect to various variables. • Be able to solve various rates of change applications. Critical Vocabulary: Derivative, Rate of Change WARM UP: Find dy/dt: 3x2y3 = 12

  6. I. Derivatives Warm Up: Find dy/dt: 3x2y3 = 12

  7. II. Applications Guidelines for Solving Related Rate Problems 1. Identify all given quantities and quantities to be determined. • Make a sketch and label your diagram • Write an equation involving the variables whose rates or change either are given or are to be determined. • Volume Formulas (Inside Cover of Book) • Area Formulas (Inside Cover of Book) • Pythagorean Theorem (when you sketch looks like a RT Δ) 3. Using implicit Differentiation, differentiate with respect to time. 4. Substitute Values as necessary. Then solve for the required rate of change.

  8. II. Applications Example 6: A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (r) of the outer ripple is increasing at a constant rate of 1 foot per second. When the radius is 4 feet, at what rate is the total area (A) of the disturbed water changing?

  9. II. Applications Example 7: Air is being pumped into a spherical at a rate of 4.5 cubic feet per minute. Find the rate of change of the radius when the radius is 2 feet.

  10. Related Rates • Objectives: • Be able to find the derivative of an equation with respect to various variables. • Be able to solve various rates of change applications. Critical Vocabulary: Derivative, Rate of Change

  11. II. Applications Example 8: A ladder 10 feet length is leaning against a brick wall. The top of the ladder is originally 8.5 feet high. The top of the ladder falls at a fixed rate of speed dy/dt. As time goes by the distance x(t) from the base of the wall to the bottom of the ladder changes. What is the rate of change of the distance x(t)?

  12. II. Applications Example 9: A baseball diamond has the shape of a square with sides 90 feet long. Suppose a player is running from 1st to 2nd at a speed of 28 feet per second. Find the rate at which the distance from home plate is changing when the player is 30 feet from second base.

More Related