+9479 y = x3 - 2x2
Take the derivative of this to find a function that will tell you the slope of the graph of that line at any point.
y' = 3x2 - 4x
Set y' = 0 to find all the points where the slope is 0.
0 = 3x2 - 4x
0 = (x)(3x - 4)
x = 0 and x = 4/3
So at x = 0 and at x = 4/3 the slope of x3 - 2x2 is 0. That means those points are maximums, minimums, or inflection points. To figure out which, take the second derivative.
y''= 6x - 4
Find y'' at x = 0
y'' = 6(0) - 4 = -4
Since y'' is negative at x=0, the graph is concave down at x = 0, so there is a max at x=0.
Find y'' at x = 4/3
y''= 6(4/3) - 4 = 8 - 4 = 4
Since y'' is positive at x = 4/3, the graph is concave up at x = 4/3, so there is a min at x = 4/3.
