Mercer County Community College

Prof. Porter

MAT111 Calculus Test 2: Derivatives

 

1. Use the definition of derivative to find f’(x) if f(x) = x(x-3) + 2
2. Find the derivatives f’(x) if
   1. f(x) = x(x-3) +2
   2. f(x) = sin(x)/x
   3. f(x) = 4xcos(3x-2)
   4. f(x) = 2xf(x) + 5x - 7
3. Give the equation of the tangent line to the function g(t) = t(t-3) at t = 2
4. Give the equation of the tangent line to the graph y = 2xy + 5x – 7 at (1,2)
5. If a spherical balloon is expanding at a rate of 2 cm/sec when it is 3 cm in diameter, what how fast is the helium filling the balloon.
6. If that same balloon should shoot strait up in the air at the rate of 8 m/sec and you run strait away at  6 m/sec. How fast is the distance between you growing when the balloon reaches 16 meters?
7. Use differentials to approximate the cubed root of 12.
8. If the error in measuring the length of a rectangle is .01 and the width is 3 times the length, then what is the error in measuring the area of the rectangle?