Prof. Porter

MAT111 Calculus Test 2: Derivatives

- Use the definition of derivative to find f’(x) if f(x) = x(x-3) + 2
- Find the derivatives
f’(x) if
- f(x) = x(x-3) +2
- f(x) = sin(x)/x
- f(x) = 4xcos(3x-2)
- f(x) = 2xf(x) + 5x - 7

- Give the equation of the tangent line to the function g(t) = t(t-3) at t = 2
- Give the equation of the tangent line to the graph y = 2xy + 5x – 7 at (1,2)
- 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.
- 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?
- Use differentials to approximate the cubed root of 12.
- 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?