Showing theres no maximum to a function

**richtea9** · November 10th 2011, 03:22 AM

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?

**FernandoRevilla** · November 10th 2011, 03:43 AM

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.

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