Math Help - Showing theres no maximum to a function

1. Showing theres no maximum to a function

I have the following function:

$f(x)=6x^2-x-2$

I've worked out the derivative of this function:

$f'(x)=12x-1$

I've also worked out the minimum:

$(\frac{1}{12}, \frac{-49}{24})$

However, I am unsure how I can prove/show that there is no maximum to this function?

2. Re: Showing theres no maximum to a function

Originally Posted by richtea9
However, I am unsure how I can prove/show that there is no maximum to this function?
If there is a relative maximum at $x_0$ , necessarily $f'(x_0)=0$ so the function has no relative maximum. If you ask for absolute maximum take into account that $\lim_{x\to +\infty}f(x)=\lim_{x\to -\infty}f(x)=+\infty$ , so $f$ has not absolute maximum either.