AP Calculus -Test- Chapter 3

Name

Chapter 3 Test

1. Find the Derivative

A. 4x3 + 3x B. 5 x C.4Öx D. -1 . x2 E. 1 . Öx F. 2e5x G. ln 3x - 7 H. 5x3 sin x I. 26x

J. 4 6x + 1 K. cos x 3x2 L. tan x M. (3x2 + x)5 N. Ösin 3x2 O. 5x2 cos x P. (3x2 + 4x)2 3x + 6 Q. log2 3x R. x6x

2. Find y',y'', and y'''.

A) 5x⁷ + 3x⁶ – x⁵ + 2x⁴ + 3x² – 12

B) cos 3x

3. Find the equation of the tangent line at P.

1. y = 3x² P = (1,3)
   

1. y = 2x – 4 . P = (4,6)
   

   
   Öx
   

4. Find where the slope of the tangent line to y = x³ - 3x² is 0.

5. A spherical balloon's radius is increasing as it is inflated. Find how fast its volume is increasing with respect to the radius at r = 10 cm.

6. An athlete's position on a field is determined by the equation 100 + 25t – 5t². Find when his velocity is 0.

7. You are the director of an action movie. In one scene, a stunt man is launched from a catapult such that his height above ground at any time is given by -16t² + 48t + 64. You will need to set up the cameras to catch appropriate moments in his flight. Find…

1. When he gets to highest point and how high he is.
   

1. When he hit's the ground, and how fast he's going when he gets there.
   

1. How high up he is when he's launched, and with what velocity he is launched.