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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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mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0do we use the quadratic formula for this one?

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0did you find the derivative?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0derivative is 1*x^2+72x*(4)*x/ (x^2+7)^2

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0from there.. x^26x+7/x^4+14x^2+49

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0and i'm left with x^26x+7

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0however, i can't factor this... so do i use quadratic formula?

mattt9
 2 years ago
Best ResponseYou've already chosen the best response.0yeah I did not check your math, however if it is correct then use the quadratic formula.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0can you try the problem also?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i want to know if its correct.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0"derivative is 1*x^2+72x*(4)*x/ (x^2+7)^2" That first term shouldn't be a 1. The derivative of 4x is not 1. I think that should fix it up for you.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0yes i must of typed it wrong. but that's exactly what i got here.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0\[\large f'(x)=\frac{\color{royalblue}{(4)}(x^2+7)(4x)\color{royalblue}{(2x)}}{(x^2+7)^2}\]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0Set it equal to zero, then multiply both sides by the denominator. Don't do long division or anything silly like that.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0yeah i ended up with x^26x+7/x^4+14x^2+49

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry website wasn't working...

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0\[\large 0=\frac{4x^228+8x^2}{(x^2+7)^2}\]Multiplying both sides by the denominator gives us,\[\large 0=4x^228+8x^2\] I don't understand how you got the x term in the middle.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0how do i get the derivative. can you show me?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0\[\large f(x)=\frac{4x}{x^2+7}\] Remember the quotient rule, it will tell us to setup the derivative like this,\[\large f'(x)=\frac{\color{royalblue}{(4x)'}(x^2+7)(4x)\color{royalblue}{(x^2+7)'}}{(x^2+7)^2}\]The blue terms are the ones we need to differentiate.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0according to the quotient rule.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0Which gives us this,\[\large f'(x)=\frac{\color{royalblue}{(4)}(x^2+7)(4x)\color{royalblue}{(2x)}}{(x^2+7)^2}\] Which simplifies to this,\[\large f'(x)=\frac{4x^228+8x^2}{(x^2+7)^2}\]Right?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0then it's 4x^228 right?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0Yes. From there you can find a critical point.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i appreciate your help a lot. i just need time to figure this out... :(

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0Yah that sounds right. So we have a couple steps now. We plug our `critical points` into the original function, and write down the \(\large f\) values they produce. Then, plug the `end points` into the original function, and write down the \(\large f\) values they produce. Then simply compare the \(\large f\) values. The largest will be your maximum. The smallest, your minimum.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0\[\large x \in\left[1,4\right]\]These are our end points, 1 and 4. The end points of our interval.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0is the first critical point: 2 radical 7/7 ?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0thats the positive criticla point that i used.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0and the f ( radical 7) is 4 radical 7?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0hope it's right :(

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0are you checking to see if i am doing the problem correct?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0very worried, please help me.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.0no the negative root should produce 2sqrt7/7 i think.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0it's not \[\frac{ 2\sqrt{7} }{ 7 }\] ??
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