Question

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

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

Answer 1

The answer is 72.578

Explanation:

Answer 2

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