# 2.1

1. Consider the parabola y = 6x – x^2

2. Find the equation of the tangent line to the curve at the given point.
4.Find the slope m of the tangent to the curve y = 6 + 4x^2 -2x^3 at the point where x = a.
5. If a ball is thrown into the air with a velocity of 33 ft/s, its height (in feet) after 6 seconds is given by y = 33t – 16t^2. Find the velocity when t = 1.
6. The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 6/t^2, where t is measured in seconds. Find the velocity times t = a, t = 1, t = 2, and t = 3.
7. Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = -5 and g’’(6) = 2. (Enter your answer as an equation in terms of y and x.)
8. If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f’(4).
9. Find f’(a). f(x) = 4x^2 -5x + 3
10. If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters) after t seconds is given by H = 10t -1.86t^2.