Verify that Rolle's Theorem can be applied to the function f (x) = x3 - 11x2 + 38x - 40 on the interval [2, 5]. Then find all values of c in the interval such that f (c) = 0. Enter the exact answers in increasing order. To enter va, type sqrt(a). C = C =Verify that the Mean Value Theorem can be applied to the function f (x) = x5 on the interval [0, 1). Then find the value of c in the interval that satisfies the conclusion of the Mean Value Theorem. Enter the exact answer. C=Find the linearization of the function f (I) = at 1 = -1. 91+8 L( I) = Find the true values of f (x) and the approximations using L () below. Round all of your answers to 3 decimal places. You can use a calculator, spreadsheet, browser, etc. to calculate the exact values. I The exact value f (E) The approximate value L (I) -1.1 Number Number -1.01 Number Number -1.001 Number NumberCompute the values of lip and rig for the function y = 321 + 5:: given a: = I} and at: = d: = 0.03. Round your answers to four decimal places, ifrequired. You can use a calculator, spreadsheet, browser, etc. to calculate y and y. dy = I Number I :13.- = I Number I Use differentials to estimate the value of 41,,,n'1.3. Compare the answer to the exact value of 4v\" 1.3. Round your answers to six decimal places, if required. You can use a calculator, spreadsheet, browser, etc. to calculate the exact value. estimate = ' Number ' exact value = ' Number ' The radius of a circle is increasing at a rate of 7 centimeters per minute. Find the rate of change of the area when the radius is 2 centimeters. Round your answer to one decimal place. The rate of change of the area is Number UnitsAssume that I and y are both differentiable functions of t and are related by the equation y = Cos (4:)- Find dy dt when I = g . given =-5 when I = dt Enter the exact answer. dy Number dt