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help help help!!!! Determine the extrema of f(x)= (4)* x/ x^2+7 below on the given interval
(a) on [1,4]
The minimum is ?? and the maximum is ??
(b) on [1,5]
The minimum is ?? and the maximum is ??
 one year ago
 one year ago
help help help!!!! Determine the extrema of f(x)= (4)* x/ x^2+7 below on the given interval (a) on [1,4] The minimum is ?? and the maximum is ?? (b) on [1,5] The minimum is ?? and the maximum is ??
 one year ago
 one year ago

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mattt9Best ResponseYou've already chosen the best response.0
is the x^2+7 all under the 4x
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
yup\[ \frac{ (4)*x}{ x^{2}+7}\]
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
and what was your derivative again?
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
\[\frac{ 1*(x ^{2}+ 7)2x(4)*x}{ (x^{2}+7) ^2 }\]
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
are you sure that is correct wouldn't the derivative of the top be 4 not 1
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
yeah explain that please
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
maybe I did get it wrong. but i assumed since 4 is a constant i didn't use it...
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
you still use the constant if it's attached to the x like that.
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
(d/dx) of 2x is 2 right?
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
oh so when you add you don't use the constant right?
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
you wouldn't use the 7 when determining the derivative of the bottom since it is not attached to an x value.
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
oh so you multiplied them which is 4x... then just fnd the derivative right>
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
for example if it is 4+x then the derivative is 1.
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
but if (4)*x you keep them as 4 and find the derivative which is 4
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
right. then your derivative simplifies to : \[\frac{ (4x^228) }{ (x^2+7)(x^2+7) }\]
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
awesome so let me do that.
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
how did you get 4x^228?
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
what happened with the 6x?
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
i thought the derivative would be 4x^2286x on the numerator
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
yeah but you wrote.. (4x2−28)/(x2+7)(x2+7)
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
yeah i know. but you had problems with the numerator. so i just showed you how i got the numerator
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
that is the full derivative.
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
anyways. you end up equation that to zero. \[\frac{ (4x^228) }{ (x^2+7)(x^2+7) }=0\]
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
the (x^2+7) cancels out and you are left with 4x^228 = 0
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
then solve for x to obtain a value for which the slope of the function is zero (a possible max or min)
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
at this point you will see that x = +root(7) = + 2.646
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
then you see that x = 2.626 is not in your given interval so you would not test this value. in the first interval of [1,4] you would test the xvalues of x = 1 x = 4 and your found x value of x = 2.626 out of these three numbers one will be highest and one will be lowest, those should be your max and min for the function respectively. Let me know if any of that is incorrect.
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
matt you make sense. are you there @mattt9
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
so we don't test the critical points correct?
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
those are the critical points.
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
a) because the intervals are [1,4] and b) intervals are from [1,5]
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
or at least 2.626 is for the function. 1 and 4 are for the interval. or maybe that terminology isn't used i can't remember but you would test all three of those points
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
i did test them all out. i wrote (a) on [1,4] The minimum is .695652 and the maximum is 1/2 (b) on [1,5] The minimum is .625 and the maximum is 1/2 but when i click submit it says one of them is wrong...
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
@mattt9 i would appreciate the help very much.
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
ummmmm what do you get when you plug in 2.626 into the fn.?
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
2.626 into the fn.?
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
the radical 7 or negative radical 7 is 2.64575
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
(4)(2.626)/(2.626^2+7) = 0.7559
 one year ago

mattt9Best ResponseYou've already chosen the best response.0
that should be your minimum for both.
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
youre right, i didn't see the negative by mistake.
 one year ago
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