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
