Expert: Paul Klarreich - 11/9/2011

Question
For each of the following, find the point(S) if any, where the relation has nay vertical tangent lines.

1. g(x)=3- cubed root of x

2. f(x)= square root of 4-x^2

3. Consider the curve by xy^2-x^3y=6. Find the x-coordinate of each point on the curve where the tangent line is vertical.

Answer
Questioner: Taylor
Country: Texas, United States
Category: Calculus
Private: No
Subject: Vertical Tangent Lines
Question: For each of the following, find the point(S) if any, where the relation has nay vertical tangent lines.

1. g(x)=3- cubed root of x

2. f(x)= square root of 4-x^2

3. Consider the curve by xy^2-x^3y=6. Find the x-coordinate of each point on the curve where the tangent line is vertical.

......................................
Let's do some translation:
Find the point(S) if any, where the relation has a vertical tangent line.
===>
Find the point(S) if any, where the GRAPH of the relation has a vertical tangent line.
===>
Find the value(s) of x, if any, where the GRAPH of the relation has a vertical tangent line.
===>
Find the value(s) of x, if any, where the slope of the tangent line is undefined.
===>
Find the value(s) of x, if any, where dy/dx is undefined.

Now do:

1. Compute the derivative, dy/dx.(You will use implicit differentiation for 3.)
2A. If dy/dx is not a fraction, stop.  dy/dx is defined for all x; no V.T. lines
2B. If dy/dx IS a fraction, set the bottom = 0 and solve.

No. 3 might be messy.  If you need more help, send me what you did and I'll see what I can do.