1. Find the equation of the tangent line to the curve f(x)= 4x2-5x when the line is parallel to the line y = 3x-5. (Full solution)
2. Find the derivative of the following 3x2=5y3 +17y . (Full solution)
3. A piece of lumber at a construction site is resting against the frame of a house on a cement floor. The lumber is 4 m long. If the bottom of the lumber slides away from the wall at a rate of 0.25 m/s, how fast is the top of the lumber sliding down the wall, when the bottom of the lumber is 2 m from the wall? (Full solution)
4. State the first principles method and the power rule for finding derivatives. Comment on the flexibility and efficiency of both.
5. What is the suggested procedure for solving a related rate problem?