Download presentation

Presentation is loading. Please wait.

1
**Derivative of a function**

2
**lim x-6 x2-36 lim x2-12x+36 x2-7x+6 lim x2-81 9-x x ⟶ 6 x ⟶ 9 x ⟶ 1**

Warm-up lim x-6 x ⟶ 6 x2-36 1 12 ∴ limit exists lim x2-12x+36 x ⟶ 1 x2-7x+6 = -5/0 , ∴ limit DOES NOT exist lim x2-81 x ⟶ 9 9-x =-18 , ∴ limit exists

3
**Definition of the Derivative**

4
**EXAMPLE: Find the derivative of f(x) = 3x2 - 2x**

f’(x) = [3(x+h)2 - 2(x+h)] - [3x2 - 2x] h f’(x) = [(3x2 +6xh + 3h2 ) - (2x+2h)] - [3x2 - 2x] h f’(x) = 3x2 +6xh + 3h2 - 2x - 2h - 3x2 + 2x h f’(x) = 6xh + 3h2 - 2h h f’(x) = (6x + 3h - 2) f’(x) = h (6x + 3h - 2) h f’(x) = (6x - 2)

5
**PRACTICE 1. f(x)= 5x- 8 2. f(x)=-3x + 9 3. f(x)= 12x + 3x - 10 5 -3 15**

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google