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
