G) 59m 0 Question 4 v l3 0/5 pts '9 2 k1,\" Given the function 9(3) = 43:3 24m2 60m, find the first derivative, g'(;v). g'lv) =i i Notice that g'(a:) = 0 when a: = 1, that is, g'(1) = 0. Now, we want to know whether there is a local minimum or local maximum at a: = 1, so we will use the second derivative test. Find the second derivative, 9"(m). 9\"($) =i i Evaluate g\"(1). g\"(1) = Based on the sign of this number, does this mean the graph of g(:c) is concave up; or concave down at a: = 1? [Answer either up or down -- watch your spelling!!] At :1: = 1 the graph of 9(3) is concave Based on the concavity of 9(m) at m = 1, does this mean that there is a local minimum or local maximum at :1: = 1? [Answer either minimum or maximum -- watch your spelling!!] At :1: = 1 there is a local 0 Question 3 v Consider the function f(m) = 1 73:2, 3 l3 0/ 5 pts The function f(:1:) = 2:1:3 + 36:32 120m + 11 has one local minimum and one local maximum. This function has a local minimum at :1: =' ' with value ' ' and a local maximum at a: = ' ' with value ' ' Check Answer Question 1 0/5 pts 2 2 1 -3 -2\\-1 2 4 5 -2 The above is the graph of the derivative f '(x). How many critical points does the original function f(x) have? Check