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

mattt9Best ResponseYou've already chosen the best response.0
did you find the derivative?
 one year ago

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

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

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

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

mattt9Best ResponseYou've already chosen the best response.0
yeah I did not check your math, however if it is correct then use the quadratic formula.
 one year ago

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

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

zepdrixBest 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.
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
yes i must of typed it wrong. but that's exactly what i got here.
 one year ago

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

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

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

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

zepdrixBest 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.
 one year ago

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

zepdrixBest 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.
 one year ago

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

zepdrixBest ResponseYou've already chosen the best response.0
Which 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?
 one year ago

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

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

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

zepdrixBest ResponseYou've already chosen the best response.0
Yah 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.
 one year ago

zepdrixBest 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.
 one year ago

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

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

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

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

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

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

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

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

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