math 148 - business calculus

5. Choose a company and do a web search to find their stock prices over the past several years. (I have found that a search via bing.com often shows a graph of the prices over time right away, but you can find this info via other search engines too.) Name of the company you chose: _________________________ a. Compute the average rate of change over a 2-year period. Let January 2015 be t=0 and p be the stock price. First date and stock price ________________ _________________ Second date and stock price _________________ __________________ Ordered pairs: _____________ _________________ AROC (rounded to two decimal places): Interpretation: b. For the company you chose, estimate the instantaneous rate of change at the beginning of your 2-year period by choosing two points close together, for instance one week apart. Interpret your answer. (Hint: When calculating the IROC, it might be helpful to remember that 1 week is 1/52 of a year.) First date and stock price ________________ _________________ Second date and stock price _________________ __________________ IROC (rounded to two decimal places): Interpretation: c. Compare your answer to the AROC. What kind of information do each of these values give you? Derivative Formulas Power Rule: d n x = nx n 1 dx Product Rule: d f (x ) g (x ) = f ' (x ) g (x ) + f (x ) g ' (x ) dx Quotient Rule: d f (x ) f ' (x ) g (x ) f (x ) g ' (x ) = dx g (x ) g (x ) 2 Chain Rule: d f (u ) = f ' (u ) du dx dx Log Rule: d ln x = 1 dx x d log b x = 1 dx x ln b Exponential Rule: d x e = ex dx d x b = b x ln b dx OR df df du = dx du dx