Name: _Calculus IDue Friday October 7, 2005E-mail to sforman@sju.eduMaple Lab #2Using Maple to Work With DerivativesExercises: Each of the following questions has to do with derivatives. Use Maple to do all calculations that you need, and to find all derivatives. Include explanations of your work in text cells. Put the work for each question underneath the question. Please also type your name at the beginning of this lab.1. Let NiMvLSUiZkc2IyUieEcsKComIiIkIiIiKiRGJ0YqRitGKyomIiInRisqJEYnIiIjRishIiJGKkYr.a. Find the derivative of f(x) by setting up the limit definition and using Maple to evaluate it. b. Find the derivative of f(x) using the Maple command D and call the derivative fprime. Use Maple to plot both functions on the same axes. Make the derivative blue and the original function red.c. Find the equation of the tangent line to f(x) when x= -1. Show two graphs using Maple. The first should show an overall graph of the function with this tangent line. The second should be on a small interval around x = -1 where the function and tangent line coincide. d. Define a function g(x) to be the tangent line to f(x) when x=-1. Compare the values of f(x) and g(x) at x = -1, -.8, and 4. Explain why sometimes the two functions are close together and sometimes they are not. 2. A graph of two functions, f and g, is shown below. (To see which function is which, you may need to right-click on the graph, and under Legend, choose Show legend). Determine which one is the derivative of which. Give your answer as either g '(x) = f(x) or f '(x) = g(x), and explain your answer. Type in complete sentences.

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3. The cost of purifying a gallon of water to a purity of x percent is NiMvLSUiQ0c2IyUieEcqJiIkKyIiIiIsJkYpRipGJyEiIkYs cents, when x is larger than or equal to 50 and less than 100.a. Define the function C(x), and use Maple to graph the function. What can you say about the sign of the derivative C'(x) from the graph of C(x)? Explain why.b. How much does it cost to make a gallon of water 75% pure? Use Maple to do the calculations and write your answer in a complete sentence.c. How fast is the cost changing when the water is 97% pure? Use Maple to do the calculations and write your answer in a complete sentence. (Round answer to the nearest hundredth).