1 / 16

Section 3.6

Section 3.6. 1. Implicitly differentiate to find dy/dx. y 3 – x 2 = 4. 2. Implicitly differentiate to find dy/dx. y 4 – x 3 = 2x. 3. Implicitly differentiate to find dy/dx. x 2 y = 8. 4. Implicitly differentiate to find dy/dx. x(y – 1 ) 2 = 6.

knox
Download Presentation

Section 3.6

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. Section 3.6 1. Implicitly differentiate to find dy/dx. y 3 – x 2 = 4

  2. 2. Implicitly differentiate to find dy/dx. y 4 – x 3 = 2x

  3. 3. Implicitly differentiate to find dy/dx. x 2y = 8

  4. 4. Implicitly differentiate to find dy/dx. x(y – 1) 2 = 6

  5. 5. Implicitly differentiate to find dy/dx.

  6. 6. Implicitly differentiate to find dy/dx and evaluate it at the given point. y 2 – x 3 = 1 at x = 2, y = 3.

  7. 7. Implicitly differentiate to find dy/dx and evaluate it at the given point. x 2 y + y 2x = 0 at x = - 2, y = 2.

  8. 8. For the following demand equation Implicitly differentiate to find dp/dx. p 2 + p + 2x = 100

  9. 9. For the following demand equation Implicitly differentiate to find dp/dx. xp 3 = 36

  10. BUSINESS: Demand Equation – A company’s demand equation is • x = (2000 – p 2 ) ½ , where p is the price in dollars. Find dp/dx when p = 50 and interpret your answer. Implicitly differentiate the given function.

  11. BUSINESS: Sales – The number of MP3 music players that a store will sell and their price p (in dollars) are related by the equation • 2x 2 = 15,000 – p 2 . Find dx/dp when p = 100 and interpret your answer.

  12. 12. BUSINESS: Work Hours - A management consultant estimates that the number h of hours per day that employees will work and their daily pay pf p dollars are related by the equation 60h5 + 2,000,000 = p3. Find dh/dp at p = 200 and interpret your answer.

  13. 13. GENERAL” Snowball - A large snowball is melting so that its radius is decreasing at a rate of 2 inches per hour. How fast is the volume decreasing at the moment when the radius is 3 inches away? [The volume if a sphere of a radius r is V = 4/3 (pie) r3 ]

  14. 14. Business: Revenue - A company's revenue from selling x units of an item is given as R = 100x – x2 dollars. If sales are increasing at the rate of 80 per day, find how rapidly revenue is growing (in dollars per day) when 400 units have been sold. R = 1000x – x2 R’ = 1000x’ – 2xx’ = x’(1000 – 2x) The quantity sold, x, is increasing at 80 per day. i.e., x’ = 80 when x = 400. R’ = 80[1000 – 2(400)] = 16,000 Therefore the company’s revenue is increasing at $ 16,000 per day.

  15. 15. Related Rates: Speeding - A traffic patrol helicopter is stationary a quarter of a mile directly above a highway, as shown below. It’s radar detects a car whose line-of-sight distance from the helicopter is half a mile and is increasing at the rate of 57 mph. Is the car exceeding the highway’s speed limit of 60 mph? 0.25

  16. 16. Business: Sales - The number x of printers cartridges that a store will sell per week and their price p (in dollars) are related by the equation x 2 = 4500 – 5p 2. If the price is falling at the rate of $1 per week, find how the sales will change if the current price is $20.

More Related