The discussion revolves around finding the X-intercept of the function F(x) = x - 12x^(1/3). Participants are exploring the implications of setting the function equal to zero to identify the X-intercept.
The conversation is active, with participants providing insights on the u-substitution method and discussing the implications of cubing terms. There is no explicit consensus on the approach to take, but guidance has been offered regarding the use of u-substitution and the interpretation of the function's behavior.
Participants are working under the constraints of homework rules, which may limit the extent of assistance they can receive. There is an emphasis on understanding the reasoning behind each step rather than simply arriving at the answer.
Airp said:Homework Statement
F(x)= x-12x1/3 Find the X-intercept
Homework Equations
X-intercept means y=0
The Attempt at a Solution
My math teacher gave plus or minus 24sqrt3 as an answer, but I have no idea how he got that! He also got 0, but I do understand that one... I just don't know how to get the 24sqrt3 Could someone help me, please?
Thank you so much! This community really is awesome!RUber said:The u-substitution is all you need. However, the answer you get is for u. x = u^3. So you will cube your answer.
There should be no reason to cube 12. That would be assuming that
##F(x)^3=(x-12x^{1/3})^3 = x^3 - 12^3 x## but that is not how powers of polynomials work.
Edit:
However, in this case, since you are assuming that F(x) = 0 (x- intercept), you will get the right solution since:
##0=x-12x^{1/3}##
##x=12x^{1/3}##
##x^3=12^3x##
##0=x^3-12^3x##
There are many ways to get to the answer...just be sure you know why you are doing things.