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

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

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

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

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

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

mattt9
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0can you try the problem also?

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

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

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

zepdrix
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0how do i get the derivative. can you show me?

zepdrix
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0according to the quotient rule.

zepdrix
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0then it's 4x^228 right?

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

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

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

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

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0yah that sounds right.

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

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

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

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

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

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