1
$\begingroup$

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

$\endgroup$
  • $\begingroup$ Yes, there is only one critical point, because the domain is $\mathbb{R}$ \ $\{0\}$ $\endgroup$ – Bijesh K.S Oct 28 '16 at 18:07
  • $\begingroup$ 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. $\endgroup$ – Masacroso Oct 28 '16 at 18:08
  • $\begingroup$ en.wikipedia.org/wiki/Critical_point_(mathematics) just go through the definition $\endgroup$ – Bijesh K.S Oct 28 '16 at 18:12
  • $\begingroup$ Thanks guys. Having a "duh" moment LOL. $\endgroup$ – Garren Miller Oct 28 '16 at 18:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.