Homework Help

Using the algorithm for curve sketching i.e first derivative and second derivatives. ...

lbawa's profile pic

Posted via web

dislike 1 like

Using the algorithm for curve sketching i.e first derivative and second derivatives.  Explain what the graph of y=x^(5/3)-2x^(2/3) would look like.

My teacher said there would be a cusp in the graph.  How would I know that? 

 

 

1 Answer | Add Yours

rcmath's profile pic

Posted (Answer #1)

dislike 2 like

Usually you have a cusp, when 

or 

i) Let's start by finding the inflection points.

``

so ``

``

Point of inflection

`` 

I will use the unsimplified y' to find y''

``

``

``

since the denominator is always non negative we only need to study the numerator.

``

``

x=4/5 falls in the firt interval, thus we know that we have a relative minimum.

ii) For the Cusp.

``

we notice that x=0 will make the denominator zero, thus y' undefined. let's study the limit at this point.

``

because the numerator will be negative, as well as the denominator.

``

because the numerator will be negative but denominator positive

Hence we have a cusp at x=0, in other words we have a vertical tangant.

 

 

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes