1. A function F is the antiderivative of f if
4.10 Antiderivatives
A function F is the antiderivative of f if
F (x) = f (x) for all x.

2. Ex 1: Find the Antiderivative.

3. NOTE: see pg. 352 for more Antiderivative Formulas
Ex 2: Find all functions g such that:

4. Ex 3: Find f such that f (0) = 1 and

5. Ex 4: Make a rough sketch of the antiderivative F, given that F(0) = 2, & the sketch of f.

6. y = f (x)

7. Ex 5: A particle has an acceleration given by a(t) = 6t + 4
Ex 5: A particle has an acceleration given by a(t) = 6t Its initial velocity is v(0) = 6 cm/s and its initial displacement is s(0) = 9 cm. Find the function s(t).

8. Position, Velocity, & Acceleration
NOTE: Acceleration due to gravity is  9.8 m/s2 OR 32 ft/s2

9. Ex 6: A ball is thrown upward with a speed of 36 ft/s from the edge of a 400 ft. cliff.
A) Find h(t) where h is height in feet & t is time in seconds. B) When does it reach its max height?
C) When does it hit the ground?

10. HW – 4.10 pg. 356 # 17 – 41 odds, 59 – 65 odds