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8-47.
Given: y2 = x − x3 : Homework Help ✎
Write an equation for
. For what value of y is there a vertical tangent to the graph?
For what values of x are there vertical tangents to the graph?
Write an equation for
.
Implicit differentiation.
Determine all y-values in which the denominator of the derivative is 0.
Use the original function to determine 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 second derivative must be written in terms of x and y only.