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mathcalculus
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help! :( finding the critical point of g(x)= (x+4)/(x1)
 one year ago
 one year ago
mathcalculus Group Title
help! :( finding the critical point of g(x)= (x+4)/(x1)
 one year ago
 one year ago

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
5/(x^22x+1)= 0
 one year ago

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

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
5/(x^22x+1)= 0
 one year ago

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

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the 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
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
right
 one year ago

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

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

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

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

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

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
graph 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
 one year ago

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

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
so 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
 one year ago

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

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

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

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
nope.
 one year ago

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

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

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

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

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
right.
 one year ago

mathcalculus Group TitleBest 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?
 one year ago
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