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UNIT 2 LESSON 5

UNIT 2 LESSON 5. QUOTIENT RULE. If you thought the product rule was bad. Function f is the QUOTIENT of functions g and h. It would be nice if the rule were. But, it is NOT!!!. Example 1 Let’s show that if f ( x ) = x 3 + x 2 – 5 x and g ( x ) = – x then. then. =. and.

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UNIT 2 LESSON 5

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  1. UNIT 2 LESSON 5 QUOTIENT RULE

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

  3. Functionfis the QUOTIENT offunctionsgandh It would be nice if the rule were But, it is NOT!!!

  4. Example 1 Let’s show that if f(x) = x3 + x2 – 5x and g(x) = – x then then = and

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

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

  7. Let’s try it in English 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.

  8. Example 1 continued FROM BEFORE if and then Quotient Rule x ≠ 0

  9. EXAMPLE 2 Iff(x) = x2 + 3x + 2 andg(x) = x + 1 then

  10. Example 2 continued Usef(x) = x2 + 3x + 2 andg(x) = x + 1 to show that ≠ but from previous slide

  11. Example 2 continued Usef(x) = x2 + 3x + 2 andg(x) = x + 1 to show that and from previous slide =

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

  13. Differentiate . State any restrictions on the domain. Example 4 Using the Quotient Rule Since x2 + 1 is always > 0 there are no restrictions

  14. Example 5 Using the Quotient Rule

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

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

  17. At what points on the curve is the tangent line horizontal? Example 7 Application 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. Example 7 Application (0, 0) y = 0 y = -5 (- 5, - 5)

  19. Complete Homework Assignment Questions 1-5

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