Download presentation

Presentation is loading. Please wait.

Published byHayden Alvarez Modified over 2 years ago

1
UNIT 2 LESSON 5 QUOTIENT RULE 1

2
2 If you thought the product rule was bad...

3
3 It would be nice if the rule were Function f is the QUOTIENT of functions g and h But, it is NOT!!!

4
4 then = and Example 1 Let’s show that if f(x) = x 3 + x 2 – 5x and g(x) = – x then

5
5 If and and so From previous slide ≠ Example 1 continued then

6
6 In this section we develop a formula for the derivative of the quotient of two functions. Quotient Rule

7
7 The bottom (g (x)) times the derivative of the top f ′ (x) minus the top (f (x)) times the derivative of the bottom g ′ (x) all over the bottom g (x) squared. Let’s try it in English

8
8 Quotient Rule x ≠ 0 Example 1 continued then and

9
9 EXAMPLE 2 If f(x) = x 2 + 3x + 2 and g(x) = x + 1 then

10
10 Use f(x) = x 2 + 3x + 2 and g(x) = x + 1 to show that but from previous slide ≠ Example 2 continued

11
11 Use f(x) = x 2 + 3x + 2 and g(x) = x + 1 to show that and from previous slide = Example 2 continued

12
12 Example 3 Using the Quotient Rule Restriction on domain x ≠ 4 Differentiate. State any restrictions on the domain.

13
13 Example 4 Using the Quotient Rule Since x is always > 0 there are no restrictions Differentiate. State any restrictions on the domain.

14
14 Example 5 Using the Quotient Rule

15
15 Example 6 Using the Quotient Rule Differentiate using the Quotient Rule.

16
16 Example 6 continued Find the slope of the tangent at P(0, ½ ) From previous slide

17
17 Example 7 Application At what points on the curve is the tangent line horizontal? The tangent line will be horizontal when the derivative = 0 2x(x + 5) = 0 x = 0 or x = -5 Points are (0, 0) and (-5, -5)

18
18 y = 0 y = -5 (0, 0) (- 5, - 5) Example 7 Application

19
19 Complete Homework Assignment Questions 1-5

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google