# In need of assistance with a specific question finding critical points

Here's the problem I've been given:

Determine all critical points for the following function: $\ f(x) = 2x^2 + {256 \over x}$

What I've done so far:

1. Find the derivative of $\ f(x)$. This is equal to $\ 4x - {256 \over x^2}$

2. Determine points at which $\ f'(x)$ equals zero or is undefined. I get two numbers: $\ f'(x)$ equals zero when $\ x = 4$ and is undefined when $\ x = 0$. These are the critical points I get for $\ f(x)$. However, the course I am taking says that there is only one critical point at $\ x = 4$.

What am I doing incorrect? Any help is much appreciated!

Thanks,

Garren

• Yes, there is only one critical point, because the domain is $\mathbb{R}$ \ $\{0\}$ – Bijesh K.S Oct 28 '16 at 18:07
• As @BijeshK.S said the domain of $f(x)$ is $\Bbb R\setminus\{0\}$. Then we dont need to consider what happen for $f'(x)$ at zero. – Masacroso Oct 28 '16 at 18:08
• en.wikipedia.org/wiki/Critical_point_(mathematics) just go through the definition – Bijesh K.S Oct 28 '16 at 18:12
• Thanks guys. Having a "duh" moment LOL. – Garren Miller Oct 28 '16 at 18:13