anonymous
  • anonymous
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 ??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
is the x^2+7 all under the -4x
anonymous
  • anonymous
yup
anonymous
  • anonymous
yup\[ \frac{ (-4)*x}{ x^{2}+7}\]

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anonymous
  • anonymous
@mattt9
anonymous
  • anonymous
and what was your derivative again?
anonymous
  • anonymous
\[\frac{ 1*(x ^{2}+ 7)-2x(-4)*x}{ (x^{2}+7) ^2 }\]
anonymous
  • anonymous
are you sure that is correct wouldn't the derivative of the top be -4 not 1
anonymous
  • anonymous
yeah explain that please
anonymous
  • anonymous
maybe I did get it wrong. but i assumed since -4 is a constant i didn't use it...
anonymous
  • anonymous
|dw:1363315804166:dw|
anonymous
  • anonymous
you still use the constant if it's attached to the x like that.
anonymous
  • anonymous
(d/dx) of 2x is 2 right?
anonymous
  • anonymous
oh so when you add you don't use the constant right?
anonymous
  • anonymous
as a random example
anonymous
  • anonymous
you wouldn't use the 7 when determining the derivative of the bottom since it is not attached to an x value.
anonymous
  • anonymous
oh so you multiplied them which is -4x... then just fnd the derivative right>
anonymous
  • anonymous
for example if it is -4+x then the derivative is 1.
anonymous
  • anonymous
but if (-4)*x you keep them as -4 and find the derivative which is -4
anonymous
  • anonymous
right. then your derivative simplifies to : \[\frac{ (4x^2-28) }{ (x^2+7)(x^2+7) }\]
anonymous
  • anonymous
awesome so let me do that.
anonymous
  • anonymous
okay
anonymous
  • anonymous
how did you get 4x^2-28?
anonymous
  • anonymous
what happened with the -6x?
anonymous
  • anonymous
what -6x
anonymous
  • anonymous
i thought the derivative would be -4x^2-28-6x on the numerator
anonymous
  • anonymous
|dw:1363317471013:dw|
anonymous
  • anonymous
that's the numerator
anonymous
  • anonymous
yeah but you wrote.. (4x2−28)/(x2+7)(x2+7)
anonymous
  • anonymous
^**
anonymous
  • anonymous
yeah i know. but you had problems with the numerator. so i just showed you how i got the numerator
anonymous
  • anonymous
that is the full derivative.
anonymous
  • anonymous
anyways. you end up equation that to zero. \[\frac{ (4x^2-28) }{ (x^2+7)(x^2+7) }=0\]
anonymous
  • anonymous
the (x^2+7) cancels out and you are left with 4x^2-28 = 0
anonymous
  • anonymous
then solve for x to obtain a value for which the slope of the function is zero (a possible max or min)
anonymous
  • anonymous
at this point you will see that x = +-root(7) = +- 2.646
anonymous
  • anonymous
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 x-values 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.
anonymous
  • anonymous
matt you make sense. are you there @mattt9
anonymous
  • anonymous
so we don't test the critical points correct?
anonymous
  • anonymous
those are the critical points.
anonymous
  • anonymous
a) because the intervals are [1,4] and b) intervals are from [1,5]
anonymous
  • anonymous
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
anonymous
  • anonymous
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...
anonymous
  • anonymous
@mattt9 i would appreciate the help very much.
anonymous
  • anonymous
ummmmm what do you get when you plug in 2.626 into the fn.?
anonymous
  • anonymous
2.626 into the fn.?
anonymous
  • anonymous
the radical 7 or negative radical 7 is 2.64575
anonymous
  • anonymous
(-4)(2.626)/(2.626^2+7) = -0.7559
anonymous
  • anonymous
that should be your minimum for both.
anonymous
  • anonymous
youre right, i didn't see the negative by mistake.
anonymous
  • anonymous
thank you!!
anonymous
  • anonymous
you areee welcome !

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