Given the function g (x) = 6x^3 + 54x^2 + 90x , find the first derivative, g'(x) .

Question

Now, we want to know whether there is a local minimum or local maximum at x = − 1 , so we will use the second derivative test. Find the second derivative, g ' ' ( x ) . g ' ' ( x ) =

Evaluate g''(−1). g''(−1)=

I need the answer for (Evaluate g''(−1). g''(−1)=)

Answer 1

g' = 18x^2 + 108x + 90 = 18(x^2+6x+5)
so there are extrema at x=-1,-5
g" = 36(x+6)
extrema are
min if g" > 0 (g concave up)
max if g" < 0 (g concave down)

Answer 2

for g"(-1)

Answer 3

eh? You have the equation for g". Evaluate it at x = -1 !!