hand written detailed solution of Q1,2,3,5 7,8 neath and clean writing needed Nothing is Missing all the information is nothing missing

Q5 (11 points) Q1 (10 points) The diagram of a rectangular prism with a square base is given below. Assume that the surface area of the prism is fixed at 216 me. Find the width and height of the prism that will maximize its volume. Find the derivative y/ = dz "y of each of the following functions. DO NOT SIMPLIFY YOUR ANSWER AFTER YOU The surface area of the pram = 2(width)' + 4 width . height. EVALUATE THE DERIVATIVE. (a) [3 points] y = . time _5 d. (b) [7 points] y = ( logs(cosz) + tane)". height width Scarred with CamScanner width Q7 (6 points) Using the information from the table below, draw the graph for a function f. Label all intercepts, horizontal and vertical mymatetels), inflection painals) for full credit. Domain of / -30, 0) U (0, DC) and y coordinates of s- intercepts off (-1. "). (. 0) Q2 (3 points) I and y coordinates of g- intercepts of f NONE Equation(s) of vertical asymptote(s) 1=0 Equation(s) of horizontal asymptote(s) 5 = -2 Find a formula for the inverse of f(x) = 5x + 2 Critical number(s) -1, 1 Open intervals where / is increasing (-20. - 1). (1. 0) 9x - 4 Open intervals where / is decreasing (-1. 0), (0, 1) x and y coordinates of all local (1. - 4) minimum(s) of f and y coordinates of all local (-1,0) maximum(s) of / Open intervals where / is concave up -3, - v2. (0, 1 Open intervals where f is concave down (-1. 0). (1. 36) z and y coordinates of all inflection (v2 -3.7) and (-v2, -0.2) point(s) of Samal with Can Scanner Q8 (12 points) Scammed with CamScanner Consider the curve given by the function /[z) with a of 3. You are given that M(s) - 2(2+2) and /"(2) - 2(2r + 9) (z-3)' Compile the following information about /(s) and it's graph. Show your work to justify your answers to parts (b) and (el. Otherwise, fill in the blanks and no justification is necessary. Answer "NONE" if the function does not display a feature listed (a) [1 point] Critical number() of / Q3 (10 points) (b] [4 points) Find the open interval(s] where / is increasing and the open interval[s) where / is decreasing. Show your work to justify- (a) [4 points] Evaluate the integral / (-6secz . tana - sec? a + e# + - -5) dx (c] [1 point) z-coordinate(s] of all local minimum(s) of f (d) (1 point] r-coordinate(s) of all local maximum(s) of J. b) [6 points] Find f(z) given that f"(x) = 72 - sin x and f'(0) = In7 . =1, , f(0) = 0. (e) [4 points) Find the open intervals where / is concave up and the open intervals where / is concave down. Show your work to justify. If) [1 point] x- coordinate(s) of all inflection pointis) of f_