Question

Make sure you show your work clearly, use calculus, and box your final answer. No work = No credit. You may use a calculator, DESMOS, notes, and book. 1. (8 points) Let y = -x3 + 6x2 - 5 a. Find all critical numbers for f(x). b. Find the absolute extrema on the interval [-1, 3). Clearly label your answers. c. Find the absolute extrema on the interval [1, 3). Clearly label your answers. 2. (6 points) Let y = 2x4-12x2+ 2 a. Find all points of inflection. Be sure to write your answer in the form (x, y) b. List the intervals on which the graph is concave upward and concave downward. 3. (1 point) If x = -3 is a critical number and f "(-3) = -65, then is x = -3 a max or a min? Briefly explain. 4. (5 points) The demand function for a brand of running shoes is given by: p = - 3x + 42 a. Find the number of shoes that will give a maximum revenue. b. What price should be set in order to reach a maximum revenue?

Answer 1

Solm: a) for Glven, f(x) = -x + 6x²-5 critical points dt zo dt = -32 +122 =0 30(-+4)=0 ► 2014 oritical points are a=014 they, b) ou the interval [113] absolute manima and minima - 3x²+12n def = -68 +12 de ² at a=of [-113 and f(0) =-5 det - 1270 dhee thes, a=0 is the point of absolute minima - absolute minima = (aif (a) = (0,-5) absolute extrema on the interval [113] Any for Lince, No critical prints are in the interval [13] absolute minima at left end point of the interval but a l in the given function Absolute minime & (aithe). = (110) Aly

function for absolute mastima but n=3 in the given f(3) = -(3)3 + 6X3²_5 3 -2754-5 = 22 .. absolute maxima = f(x)) - (3,82) Ana SAN