Calculus I reviewExercises: 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) 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.b. 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. Maple Commands for Riemann Sums and the int comman.To load the programs for Riemann sums, you first need to enter the student package:with(student);

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Notice that it shows you a list of the names of all the commands available. The ones we will be interested in are leftbox, leftsum, rightbox, rightsum, middlebox, and middlesum. We will also use the int command. You can use the online help to get help with any of these. The basic syntax is also given below.f := x -> x^2 - 6*x;

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Middle, left and rightbox commands graph a function with the using the midpoints or the left and right endpoints as the heights of the rectangles. We specify the function, the range of x values, and also how many boxes to use.leftbox(f(x),x=1..9,6); rightbox(f(x), x=1..9,6); middlebox(f(x),x=1..9,6);

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The middle, left, and rightsum commands give the sigma notation form of the area within the boxes shown above. Using evalf() you can get a decimal value for the sum.leftsum(f(x),x=1..9,6); evalf(%); rightsum(f(x),x=1..9,6); evalf(%); middlesum(f(x),x=1..9,6); evalf(%);

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The int command will attempt to integrate the function. You can do either definite or indefinite integrals.int(f(x),x=1..9); int(f(x),x);

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Exercises1) create the graph of left and right boxes for f(x) = x^3 - 6x^2 + 12 from 1 to 4 with 6 intervals, which do you think is the most accurate.2) Create the sum of the areas of the rectangles for the left and right boxes above. Calculate the decimal values of the sums.3) Use the int command to find the true value.4) In the example above why is the sum sometimes from 0 to 5 and sometimes from 1 to 6.5) Calculate accurate values for these functions by any means necessary.a) NiMtSSRJbnRHSShfc3lzbGliRzYiNiQqJCwmSSJ4R0YmIiIjISImIiIiISIiL0YqO0YtIiImb) NiMtSSRJbnRHSShfc3lzbGliRzYiNiQqJC1JJGV4cEc2JEkqcHJvdGVjdGVkR0YsRiU2IywkKiRJInhHRiYiIiMiIiQhIiIvRjA7IiIiIiImc) NiMtSSRJbnRHSShfc3lzbGliRzYiNiQqJiwmIiIiRioqJC1JJHNpbkc2JEkqcHJvdGVjdGVkR0YvRiU2I0kieEdGJiIiIyEiIkYqLUkkY29zR0YuRjBGKkYxd)NiMtSSRJbnRHSShfc3lzbGliRzYiNiQqJi1JI2xuRzYkSSpwcm90ZWN0ZWRHRixGJTYjLUkkc2luR0YrNiNJInhHRiYiIiItSSRjb3NHRitGMEYyL0YxOyIiIUYy