CPM Homework Help : APCALC Problem 8-47

Given: y² = x − x³ : Homework Help ✎

Write an equation for $\frac { d y } { d x }$ .
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 $\frac { d ^ { 2 } y } { d x ^ { 2 } }$ .

Hint (a):

Implicit differentiation.

Hint (b):

Determine all y-values in which the denominator of the derivative is 0.

Hint (c):

Use the original function to determine the corresponding x-value for each y-value you found in part (b).

Hint (c):

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!)

Hint (d):

The second derivative must be written in terms of x and y only.

$\text{If }\frac{dy}{dx}\text{ appears in the second derivative, substitute it with the value you found in part (a).}$