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