How would you solve these?

1. Use the limits definition lim f( xth ) - f(x ) to find an expression for the derivative to the functions; h-+0 h a. f(x) = 3x b. f (x ) = 3 / x c. f (x) = 3x2 2. a. Use the limits definition lim / (X+h) - f(x) - to find an expression for the derivative to the curve y = (1/3)x3. h b. Using your answer to a) find the slope of the tangent to the curve y = (1/3)x3 to complete the following table. X Slope of tangent -3 -2 -1 0 N 3 3. a. After looking closely at the problems and solutions presented in this activity, describe the patterns that you see emerge as you find the derivatives of simple functions like y = x2, y = x3, and y = xory= x1. b. Using the patterns that you described in a), find the function that would produce a derivative of y = x. Prove your results. 4. a. Find an expression for the instantaneous rate of change of distance with respect to time (velocity) of a falling object if s = -4.9t2 (where s is distance (meters) and t is time (seconds)). (Ignore the effect of air resistance) b. Use your answer for a) to find the velocity at the times listed on the table below. Time Velocity 1 sec 5 sec 1 min