1. ## Curve Analysis (y=x-3x^1/3)

My teacher has given some test prep/homework questions. She says fully analyze them which means find the intercepts, symmetry, asymptotes, intervals of inc/dec, local max and min, inflection points, and concavity. Here are a couple of questions from the sheet. The first one I've gotten part way through (I put up my rough copy of it) and the second one I can't get because of the double root.

Here's my rough copy of the attempt at solution for the first one but I know that parts of it are wrong:

RE:

#17.

3. ## #21 Part #1:

RE: #21 Part #1:

4. ## #21 Part #2:

RE:#21 Part #2:

5. I got a couple of questios. For the first one (#17):
Is there no point of inflection?
And when I plugged in -1, I get f(-x)= f(x) therefore is the function not symmetric about the x-axis instead of origin?

For the 2nd one (#21), I see that there isn't a point of inflection but is it symmetric about the origin or x-axis?

6. Originally Posted by SportfreundeKeaneKent
I got a couple of questios. For the first one (#17):
Is there no point of inflection?
And when I plugged in -1, I get f(-x)= f(x) therefore is the function not symmetric about the x-axis instead of origin?

For the 2nd one (#21), I see that there isn't a point of inflection but is it symmetric about the origin or x-axis?