# Unfamiliar Cubed Root Function

• Oct 22nd 2012, 06:50 AM
Biff
Unfamiliar Cubed Root Function
I'm in Calculus AB and we are currently exploring the rules of derivatives. One function that they give, represented in the transcript of the lesson as $y = \sqrt[3]{x^2} + 1$ is first depicted in the attachment.

What the transcript gives and what the image shows are two different formats; what exactly does the format shown on the image signify and how do I plot this on my TI-83 graphing calculator?

• Oct 22nd 2012, 07:40 AM
ebaines
Re: Unfamiliar Cubed Root Function
I can only guess that in their attempt to write the cube root symbol:

Attachment 25339
the graphic got messed up. But the plot on the graph itself is correct. As for your graphing calculator - recall that taking the cube root of a number is the same as raising it to the 1/3 power, so $\sqrt[3] {x^2}$ is the same as $x^{2/3}$.
• Oct 22nd 2012, 08:05 AM
Biff
Re: Unfamiliar Cubed Root Function
Quote:

Originally Posted by ebaines
I can only guess that in their attempt to write the cube root symbol:

Attachment 25339
the graphic got messed up. But the plot on the graph itself is correct. As for your graphing calculator - recall that taking the cube root of a number is the same as raising it to the 1/3 power, so $\sqrt[3] {x^2}$ is the same as $x^{2/3}$.

Thanks ebaines - I think you are correct. Later in the lesson it showed the limit difference quotient with h approaching zero, except the right arrow was replaced with an ® symbol.

Since it is the same, the $x^{2/3}$ makes perfect sense now.

Thanks!