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mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0i used the quotient rule!

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0i got my critical point 5 and 1 but it's wrong :(

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1i doubt there are any

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1the derivative is \(\frac{5}{(x1)^2}\)

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1a fraction is only zero if the numerator is zero this numerator is \(5\)

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0right so when i get to this: 5/(x^22x+1)= 0 what do i do?

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1the denominator is positive for all values of \(x\) except for \(x=1\) where both it, and the original function are undefined the numerator is negative that tells you the function is always decreasing

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1you may remember what such a thing looks like from a pre  calc course

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0ok but then why isn't 5 considered a critical point?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0i know 1 gives you undefined.

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1a critical point is not the numerator a critical point is a number \(a\) where either \(f'(a)=0\) or \(f'(a)\) does not exist

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0you mean the denominator?

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1graph your derivative you will see that it never crosses the \(y\) axis, that it always lives below it i.e. it is always negative if you graph your original function, you will see that it is always decreasing

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0i did, but what i don't understand why it has no critical point.

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0okay but in this question im not allowed to use the calculator.

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1well, because it doesn't does \(f(x)=2x+1\) have a critical point?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0so if i can't graph it, how do can i automatically tell there is no critical point by looking at the derivative 5/(x^22x+1)= 0

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1of course it doesn't, because for \(f(x)=2x+1\)you have a line that is always increasing

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1when is a fraction equal to zero?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0oh no it doesn't.

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0and 0 does not multiply 5..

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1is \(\frac{5}{x}=0\) solvable?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0i think i got it...

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1right, and neither is \(\frac{5}{(x1)^2}\)

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0thanks @satellite73 :)

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1how about \(e^x\)? is that ever zero? yw

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1no, \(e^x>0\) for all \(x\) \(e^1=e\) not zero

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1the function \(f(x)=e^x\) is strictly increasing.

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0@satellite73 i have a question: how come 5/(x1)=0 is not a critical point and 4/15 is?
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