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.

On a homework problem, I got the wrong answer and figured out what to put in for it to be marked correct (online homework), but I am unsure why it is right.

The problem is to find the critical numbers for $f(x)=x^{-5}\log x$. Critical numbers occur where the derivative is 0 or undefined, so the first step is to find the derivative.

Product rule: $-5(x^{-6})\ln(x) + (x^{-5})(1/x)$

Simplify: $-5(x^{-6})\ln(x) + (x^{-6})$

Factor out $(x^{-6})$: $(x^{-6})(-5\ln(x)+1)$

$x^{-6}=1/(x^6)$ which will be undefined at $0$, so that should be part of the list of critical numbers.

Now to find zeros of $-5\ln(x)+1$: $-5\ln(x)+1=0$, $1=5\ln(x)$, $1/5=\ln(x)$, $x=e^{1/5}$.

I put in the list $0,e^{1/5}$ and it was marked incorrect.

On a hunch I removed $0$ from the list. My answer was marked correct.

Isn't $f'(x)$ undefined at $x=0$, or am I missing something? I have been marked correct on other answers which listed points where the derivative is not defined, so I am sure my definition of critical numbers is correct.

share|improve this question
    
"wolframalpha.com/input/?i=Plot%5Bx%5E%28-5%29*Log%5Bx%5D%5D" (hint) –  Amzoti Nov 14 '12 at 2:13
    
So f(x) is undefined at 0... I don't understand the significance of this. f'(x) is still undefined at 0. –  Big Endian Nov 14 '12 at 2:18

1 Answer 1

up vote 4 down vote accepted

Critical numbers occurs where the function is defined and the derivative is zero or undefuned. Since the function isn't defined at $x=0$, it can't have a critical point there.

share|improve this answer
    
Ahhhh, I didn't know that extra part of the definition. Thank you! –  Big Endian Nov 14 '12 at 2:34

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.