Raymond B. answered • 08/19/23
Math, microeconomics or criminal justice
graph has 3 zeros or x intercepts: 1, -3, and 7
F(x) = (x-1)(x+3)(x-7) = (x^2+2x-3)(x-7) = x^3-5x^2-17x+21
F'(x) = 3x^2 -10x -17 = 0
extrema = x = 10/6 +/- (1/6)sqr(100+12(17)), = turning points where the curve changes from increasing to decreasing and vice versa
y intercept = -17 the point (0,-17)
x intercepts are the points (1,0), (-3,0) and (7,0)
end behavior is approaching infinity as x approaches infinty
and approaches negative infinity as x approaches negative infinity
F"(x) = 6x -10 = 0
x= 10/6 = 5/3 = the point (5/3,
y = (x-1)(x+3)(x-7) = (5/3-1)(5/3+3)(5/3-7) = (2/3)(14/3)(-16/3) = -28(16)/27 = - 448/27= about 16.59
= where concavity changes from concave down to concave up = the inflection point
use a graphing calculator
