2 Consider the function f (z) = z + 15:: 3 _ [a] Find the domain of g]. Domain: ' [b] Give the horizontal and vertical asymptotes of f {2], if any. Enter the equations for the asymptotes. horizontal asymptote: vertical asymptote: to] Give the intervals of increase and decrease of f (z). Note: Use the letter U for union. If the function is never increasing or decreasing, enter NA increasing: decreasing: ' _ ' [d] Give the local maximum and minimum values off(z)_ H l l i=1 l ' r('' )= [e] Give the intervals ofconcavitv off(z)_ concave upward: /\\ concave downward: [f] Give the inection points of f (z). Use differentials to estimate the value of V/16.3. Compare the answer to the exact value of The radius of a circle is increasing at a rate of 9 centimeters per minute. Find the rate of change of the area when the radius is 3 centimeters. 4/16.3 Round your answer to one decimal place. Round your answers to six decimal places, if required. The rate of change of the area is Number Units estimate = Number exact value = Number A farmer wants to fence a rectangular area of 72 square feet next to a river. Find the length and width of the rectangle which uses the least amount of fencing if no fencing is needed along the river. Assume the length of the fence runs parallel to the river. Assume that I and y are both differentiable functions of t and are related by the equation y = cos (4x) Length: Number feet dy Find when I = . g. given dt = -6 when = = Width: Number feet Enter the exact answer. dy d+ = Number Verify that Rolle's Theorem can be applied to the function f (x) = x3 - 6x2 + 11x - 6 on the interval [1, 3]. Then find all values of c in the interval such that f' (c) = 0. Enter the exact answers in increasing order. Find two numbers with difference 74 and whose product is a minimum. C = Enter your answers in increasing order. First number: Number Second Number: Number Compute the values of dy and Ay for the function y = est + 2x given a = 0 and Ax = dx = 0.04. Round your answers to four decimal places, if required. dy = Number Ay = Number