The x-value of the local maximum and minimum can be found by differentiating the equation and equating the derivative to 0.
dg/dx = 9x² + 6x -30
0 = 9x² + 6x -30
Solving for x,
x = 1.5 , x = -2.2
Now we check to see which is the local maximum and minimum by putting the values into the original equation:
g(1.5) = -4.125
g(-2.2) = 72.576
Thus, the local maximum is at x = -2.2 and has a value of 72.576