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UNIT 2 LESSON 5 QUOTIENT RULE 1. 2 If you thought the product rule was bad...

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Presentation on theme: "UNIT 2 LESSON 5 QUOTIENT RULE 1. 2 If you thought the product rule was bad..."— Presentation transcript:

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


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