Given: y2 = x − x3 :
For what value of y is there a vertical tangent to the graph?
Find all y-values in which the denominator of the derivative = 0.
For what values of x are there vertical tangents to the graph?
Use the original function to find the corresponding x-value for each y-value you found in part (b).
There will be three values of x that work. That means there will be three coordinate points in which the slope is vertical: ( ____, 0 ), ( ____, 0 ) and ( ____, 0 ). (Obviously, this is NOT a function!)
The 2nd-derivative must be written in terms of x and y only.