2.1-2.4 Review Packet

AP Calculus
2.1 – 2.4 Review problems
Name__________________________
1.)
Find the derivative using the limit definition for f(t) = t2 + 3 at the point (-2, 7)
2.)
Use the alternate form of the definition of the derivative to find f ′(c ) if f ( x ) = ( x − 6 )
and c = 6.
3.)
Find the slope of the tangent line for f ( x ) = 3 x − 5 at the point (3, 2).
4.)
Write an equation of the line tangent to f ( x) =
x4 + 3
at the point (0, -3).
2x −1
2/3
8
dy
if y =
dx
(6 x − 2)3
5.)
Find
6.)
Find the derivative of f ( x ) =
7.)
The height s (in feet) at time t (in seconds) of a silver dollar dropped from the top of the
Washington Monument is s(t) = -16t2 + 555
1 + sin x
1 − sin x
(a)
Find the average velocity on the interval [2, 3]
(b)
Find the instantaneous velocity at 3 seconds.
(c)
How long will it take for the dollar to hit the ground?
(d)
Find the velocity of the dollar when it hits the ground.
8.)
A ball is tossed in the air and its height in feet above the ground after it is thrown is given by:
h(t) = -16t2 + 96t + 6 where t is measured in seconds.
(a)
What is the average velocity of the ball in the first second?
(b)
Find the instantaneous velocity at t = 1.
(c)
At what time does the ball reach its maximum height?
(d)
What is the maximum height?
dy
for f ( x) =
dx
(
)
2 x + 1 ( x3 )
9.)
Find
10.)
Is the following function continuous? Differentiable? Why or why not?
f ( x) =
 x5 − 4 x 2

1 3
2
 x − 2x
3
x ≤1
x >1