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mathcalculus
 2 years 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 ??
mathcalculus
 2 years 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 ??

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mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0is the x^2+7 all under the 4x

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

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0and what was your derivative again?

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

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0are you sure that is correct wouldn't the derivative of the top be 4 not 1

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0yeah explain that please

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

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0you still use the constant if it's attached to the x like that.

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0(d/dx) of 2x is 2 right?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0oh so when you add you don't use the constant right?

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0you wouldn't use the 7 when determining the derivative of the bottom since it is not attached to an x value.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0oh so you multiplied them which is 4x... then just fnd the derivative right>

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0for example if it is 4+x then the derivative is 1.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0but if (4)*x you keep them as 4 and find the derivative which is 4

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0right. then your derivative simplifies to : \[\frac{ (4x^228) }{ (x^2+7)(x^2+7) }\]

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0awesome so let me do that.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0how did you get 4x^228?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0what happened with the 6x?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i thought the derivative would be 4x^2286x on the numerator

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0yeah but you wrote.. (4x2−28)/(x2+7)(x2+7)

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0yeah i know. but you had problems with the numerator. so i just showed you how i got the numerator

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0that is the full derivative.

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0anyways. you end up equation that to zero. \[\frac{ (4x^228) }{ (x^2+7)(x^2+7) }=0\]

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0the (x^2+7) cancels out and you are left with 4x^228 = 0

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0then solve for x to obtain a value for which the slope of the function is zero (a possible max or min)

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0at this point you will see that x = +root(7) = + 2.646

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0then 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.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0matt you make sense. are you there @mattt9

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so we don't test the critical points correct?

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0those are the critical points.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0a) because the intervals are [1,4] and b) intervals are from [1,5]

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0or 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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i 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...

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0@mattt9 i would appreciate the help very much.

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0ummmmm what do you get when you plug in 2.626 into the fn.?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.02.626 into the fn.?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0the radical 7 or negative radical 7 is 2.64575

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0(4)(2.626)/(2.626^2+7) = 0.7559

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0that should be your minimum for both.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0youre right, i didn't see the negative by mistake.
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