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mathcalculusBest ResponseYou've already chosen the best response.0
i used the quotient rule!
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
i got my critical point 5 and 1 but it's wrong :(
 6 months ago

satellite73Best ResponseYou've already chosen the best response.1
i doubt there are any
 6 months ago

satellite73Best ResponseYou've already chosen the best response.1
the derivative is \(\frac{5}{(x1)^2}\)
 6 months ago

satellite73Best ResponseYou've already chosen the best response.1
a fraction is only zero if the numerator is zero this numerator is \(5\)
 6 months ago

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

satellite73Best 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
 6 months ago

satellite73Best ResponseYou've already chosen the best response.1
you may remember what such a thing looks like from a pre  calc course
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
ok but then why isn't 5 considered a critical point?
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
i know 1 gives you undefined.
 6 months ago

satellite73Best 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
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
you mean the denominator?
 6 months ago

satellite73Best 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
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
i did, but what i don't understand why it has no critical point.
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
okay but in this question im not allowed to use the calculator.
 6 months ago

satellite73Best ResponseYou've already chosen the best response.1
well, because it doesn't does \(f(x)=2x+1\) have a critical point?
 6 months ago

mathcalculusBest 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
 6 months ago

satellite73Best 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
 6 months ago

satellite73Best ResponseYou've already chosen the best response.1
when is a fraction equal to zero?
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
oh no it doesn't.
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
and 0 does not multiply 5..
 6 months ago

satellite73Best ResponseYou've already chosen the best response.1
is \(\frac{5}{x}=0\) solvable?
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
i think i got it...
 6 months ago

satellite73Best ResponseYou've already chosen the best response.1
right, and neither is \(\frac{5}{(x1)^2}\)
 6 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
thanks @satellite73 :)
 6 months ago

satellite73Best ResponseYou've already chosen the best response.1
how about \(e^x\)? is that ever zero? yw
 6 months ago

satellite73Best ResponseYou've already chosen the best response.1
no, \(e^x>0\) for all \(x\) \(e^1=e\) not zero
 6 months ago

satellite73Best ResponseYou've already chosen the best response.1
the function \(f(x)=e^x\) is strictly increasing.
 6 months ago

mathcalculusBest 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?
 6 months ago
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