What is the local maximum value of the function g(x)=3x^3+5x^2-17x-21?

First find the derivative
g'(x) = 9x^2 + 10x - 17

g'(x) = 0 at turning points on the graph.

9x^2 + 10x - 17 = 0

x = 0.927 , -2.037

turning points are at these values of x

To find the maximum one  find the second derivative:-

g" (x) = 18x + 10 

when x = 0.927   g"(x) is  positive   = Minimum
when x = -2.037  g"(x) is negative  = Maximum

There is a local maximum when g(x) = 3(-2.037)^3 + 5(-2.037)^2 - 17(-2.037) - 21  =  9.019  to nearest thousandth Answer