Answer Happy

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 =∼1​. (Hint - It might be helpful to remember that, although y=∼1​ is written as a rational function, it can also be expressed as a power function. That is, it can be expressed in the form y=xn ) b. Using the patterns that you described in a), find the function that would produce a derivative of y=x. Prove your results. 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.