1 / 16

Do Now

Do Now. Find the tangents to the curve at the points where the slope is 4. What is the smallest slope of the curve? At what value of x does the curve have this slope?. Product and Quotient Rules. Section 3.3b. Do Now.

harlow
Télécharger la présentation

Do Now

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. Do Now Find the tangents to the curve at the points where the slope is 4. What is the smallest slope of the curve? At what value of x does the curve have this slope?

  2. Product and Quotient Rules Section 3.3b

  3. Do Now Find the tangents to the curve at the points where the slope is 4. What is the smallest slope of the curve? At what value of x does the curve have this slope? The derivative: Slope 4, points (1,2) and (–1,–2). Find where the slope is 4: Tangent lines: For smallest slope, minimize The smallest slope is 1, and occurs at x = 0. Graphical support???

  4. As we learned last class, the derivative of the sum of two functions is the sum of their derivatives (and the same holds true for differences of functions). Is there a similar rule for the product of two functions? Let The derivative: However, We need to derive a new rule for products…

  5. Let The derivative: Subtract and add u(x + h)v(x) in the numerator:

  6. Let The derivative:

  7. Rule 5: The Product Rule The product of two differentiable functions u and v is differentiable, and To find the derivative of a product of two functions: “The first times the derivative of the second plusthe second times the derivative of the first.”

  8. How about when we have a quotient?... The derivative: Subtract and add v(x)u(x) in the numerator:

  9. How about when we have a quotient?... The derivative:

  10. Rule 6: The Quotient Rule At a point where , the quotient of two differentiable functions is differentiable, and To find the derivative of a quotient of two functions: “The bottom times the derivative of the top minus the top times the derivative of the bottom, all divided by the bottom squared.”

  11. Practice Problems Find if Let’s use the product rule with and Any other method for finding this answer?

  12. Practice Problems Differentiate Use the quotient rule with and Graphical support:

  13. Practice Problems Let be the product of the functions u and v. Find if From the Product Rule: At our particular point:

  14. Practice Problems Suppose u and v are functions of xthat are differentiable at x = 2. Also suppose that Find the values of the following derivatives at x = 2. (a)

  15. Practice Problems Suppose u and v are functions of xthat are differentiable at x = 2. Also suppose that Find the values of the following derivatives at x = 2. (b)

  16. Practice Problems Suppose u and v are functions of xthat are differentiable at x = 2. Also suppose that Find the values of the following derivatives at x = 2. (c)

More Related