Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm trying to find the concavity and inflection points to this equation:

$f(x) = 3x^3 - x^2 + 2x - 7$

I've taken the derivative which is: $9x^2 - 2x + 2$, but it's not factorable so how would I find the concavity of this question?

share|improve this question

2 Answers 2

To study the concavity, you need the second derivative of $f(x)$, which is easy to find. It is a linear function, and you will find it straightforward to determine where it changes from negative to positive.

Remark: If you wanted to determine local maxima and minima (which you were not asked about), then indeed you would be interested in the solutions of $f'(x)=0$. You could then use the Quadratic Formula to find the roots of $f'(x)$. In our particular case, $f'(x)=0$ has no real solutions.

One cannot expect that all quadratics will factor nicely: most of them don't. Soon, if not already, it will be taken for granted that you know the Quadratic Formula.

share|improve this answer

There is a formula to find the roots of a second order polinomial. Use it to factorize the derivative.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.