# Parallel Tangent

• Feb 12th 2011, 08:44 AM
youngb11
Parallel Tangent
Not sure if this belongs in pre-calc or not but I guess it's better safe than sorry.

I'm trying to determine the values of x so that the tangent to the function $\displaystyle y=3/x^{(1/3)}$ is parallel to the line $\displaystyle x+16y+3=0$

What I did was set the derivative of the function equal to the slope of the line (which is 1), but I got a different answer than the book. Can anyone tell me if I'm doing anything wrong.

$\displaystyle 1=-1/x^{(4/3)}$
• Feb 12th 2011, 08:56 AM
Plato
Quote:

Originally Posted by youngb11
I'm trying to determine the values of x so that the tangent to the function $\displaystyle y=3/x^{(1/3)}$ is parallel to the line $\displaystyle x+16y+3=0$

Solve $\displaystyle \displaystyle\frac{{ - 1}}{{\sqrt[3]{{x^4 }}}} = \frac{{ - 1}}{{16}}$
• Feb 12th 2011, 08:58 AM
youngb11
Quote:

Originally Posted by Plato
Solve $\displaystyle \displaystyle\frac{{ - 1}}{{\sqrt[3]{{x^4 }}}} = \frac{{ - 1}}{{16}}$

Ah, thanks a lot! I overlooked that 16 >.<. Thanks again!