What is the local maximum value of the function? (Round answer to the nearest thousandth.)

g (x) = 3x^3 + 3x^2 - 30x + 24

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