Raymond B. answered • 09/23/20
Math, microeconomics or criminal justice
infinity
there is no maximum,
as x approaches infinity or negative infinity, F(x) approaches infinity. It increases without bound
maybe you meant what is the minimum? which is also the vertex
take the derivative
14x-6 = 0
x=6/14 = 3/7
plug back into the quadratic
7(3/7)^2 -6(3/7) -13 = 9/7 -18/7 -13 = -9/7 - 13 = -14 2/7 is the minimum value or the vertex of an upward opening parabola
Or maybe you did mean maximum but left out a negative sign for the coefficient of the 2nd degree term?
then
F(x)=-7x^2-6x-13. This is a parabola opening downward
take the derivative and set = 0
-14x-6=0
x=-3/7
plug into the quadratic
-7(-3/7)^2-6(-3/7)-13
-3/7+18/7-13 =
15/7-13 = -10 6/7 is the maximum which is also the parabola's vertex
