Raymond B. answered • 03/04/21
Tutor
5
(2)
Math, microeconomics or criminal justice
f(0) = -1, f(-1) = 0, 0 is a root f(1) = -2. You could say f(x) has a root in the interval (-2,0) x=-1
f(2) = 3 There's another root in the interval (1,2) maybe around x = 1.5
x^3 -2x -1 has derivative 3x^2 -2 = 0
x^2 = 2/3
x = + or - sqr(2/3) are local extrema = about + or - 0.82
f(.82) =.209
f(-.82) = .09 there are two roots in the interval (-2,0), one is x=-1 and the other is near x=-.82
a 3rd root is in the interval (1,2) because f(1) and f(2) are opposite signs, so the graph has to intersect the x axis somewhere in between.
