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 ??
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
do we use the quadratic formula for this one?
anonymous
  • anonymous
did you find the derivative?
anonymous
  • anonymous
derivative is 1*x^2+7-2x*(-4)*x/ (x^2+7)^2

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More answers

anonymous
  • anonymous
from there.. x^2-6x+7/x^4+14x^2+49
anonymous
  • anonymous
then i = to 0
anonymous
  • anonymous
and i'm left with x^2-6x+7
anonymous
  • anonymous
however, i can't factor this... so do i use quadratic formula?
anonymous
  • anonymous
yeah I did not check your math, however if it is correct then use the quadratic formula.
anonymous
  • anonymous
can you try the problem also?
anonymous
  • anonymous
i want to know if its correct.
zepdrix
  • zepdrix
"derivative is 1*x^2+7-2x*(-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.
anonymous
  • anonymous
yes i must of typed it wrong. but that's exactly what i got here.
zepdrix
  • zepdrix
\[\large f'(x)=\frac{\color{royalblue}{(-4)}(x^2+7)-(-4x)\color{royalblue}{(2x)}}{(x^2+7)^2}\]
anonymous
  • anonymous
then after..
zepdrix
  • zepdrix
Set it equal to zero, then multiply both sides by the denominator. Don't do long division or anything silly like that.
anonymous
  • anonymous
yeah i ended up with x^2-6x+7/x^4+14x^2+49
anonymous
  • anonymous
??
zepdrix
  • zepdrix
Sorry website wasn't working...
zepdrix
  • zepdrix
\[\large 0=\frac{-4x^2-28+8x^2}{(x^2+7)^2}\]Multiplying both sides by the denominator gives us,\[\large 0=-4x^2-28+8x^2\] I don't understand how you got the x term in the middle.
anonymous
  • anonymous
how do i get the derivative. can you show me?
zepdrix
  • zepdrix
\[\large f(x)=\frac{-4x}{x^2+7}\] 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.
anonymous
  • anonymous
yeah
anonymous
  • anonymous
according to the quotient rule.
zepdrix
  • zepdrix
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,\[\large f'(x)=\frac{-4x^2-28+8x^2}{(x^2+7)^2}\]Right?
anonymous
  • anonymous
oh ok thank u!
anonymous
  • anonymous
then it's 4x^2-28 right?
zepdrix
  • zepdrix
Yes. From there you can find a critical point.
anonymous
  • anonymous
radical + or -7
anonymous
  • anonymous
?
anonymous
  • anonymous
@zepdrix
anonymous
  • anonymous
i appreciate your help a lot. i just need time to figure this out... :(
zepdrix
  • zepdrix
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.
zepdrix
  • zepdrix
\[\large x \in\left[1,4\right]\]These are our end points, 1 and 4. The end points of our interval.
anonymous
  • anonymous
is the first critical point: -2 radical 7/7 ?
anonymous
  • anonymous
thats the positive criticla point that i used.
anonymous
  • anonymous
@zepdrix
zepdrix
  • zepdrix
yah that sounds right.
anonymous
  • anonymous
and the f (- radical 7) is 4 radical 7?
anonymous
  • anonymous
hope it's right :(
anonymous
  • anonymous
are you checking to see if i am doing the problem correct?
anonymous
  • anonymous
very worried, please help me.
zepdrix
  • zepdrix
no the negative root should produce 2sqrt7/7 i think.
anonymous
  • anonymous
?
anonymous
  • anonymous
it's not \[\frac{ -2\sqrt{7} }{ 7 }\] ??

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