Given function g(x)= 8x^3 - 108x^2 + 480x, find the first

Last updated: 8/11/2022

Given function g(x)= 8x^3 - 108x^2 + 480x, find the first derivative, g'(x)____________ Notice that g'(x) = 0 when x = 4, that is, g'(4) = 0. Now, we want to know whether there is a local minimum or local maximum at = 4, so we will use the second derivative test. Find the second derivative, g''(x). g''(x)_______________ Evaluate g''(4) g''(4)=_________________ Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at= 4? [Answer either up or down -- watch your spelling!!] At x= 4 the graph of g(x) is concave_____________ Based on the concavity of g(x) at x = 4, does this mean that there is a local minimum or local maximum at x= 4? [Answer either minimum or maximum -- watch your spelling!!) At = 4 there is a local____________