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PLEASE HELP! :( The curve C has equation y={a(xa)^2}/x^24a^
where a is a positive constant. Show that C has one maximum point and one minimum point and find their coordinates.
 one year ago
 one year ago
PLEASE HELP! :( The curve C has equation y={a(xa)^2}/x^24a^ where a is a positive constant. Show that C has one maximum point and one minimum point and find their coordinates.
 one year ago
 one year ago

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myininayaBest ResponseYou've already chosen the best response.2
Find y' Set y' equal to 0 Solve y'=0 for x to get the critical numbers. Then we will determine if the critical numbers are max or mins or neither.
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
\[y={a(xa)^2}\div x^24a^2\]
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
I couldnot solve y'=0. I TRIED! :(
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
What did you get for y'
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
Oh and we also need to find where y' does not exist
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
a(xa)^2(2x8a)(x^24a^2)(2ax2a^2)=0
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
hmmm.... You know a is a constant right?
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
Derivative of a is 0. Derivative of any constant *a is 0.
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
a^2 is also a constant since a is a constant (a^2)'=0
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
Oops. Now I get it. O_o
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
And don't forget the quotient rules is : \[y'=\frac{ (\text{ derivative of top }) \cdot (\text{ bottom } )  ( \text{ derivative of bottom } ) \cdot ( \text{ top } )}{(bottom)^2}\]
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
Can you please show me what exactly y' would be? All these 'a' and brackets have confused me. :(
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
@experimentX : Can you please help me with this question?
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
\[y=\frac{a(xa)^2}{x^24a^2}\] \[ \text{ What is } [a(xa)^2]' \text{ equal to? }\] \[ \text{ What is } [x^24a^2]' \text{ equal to?}\]
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
For my first question, a is a constant multiple. We can just bring that down and look at differentiating (xa)^2 by using chain rule.
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
For my second question, 4a^2 is just a constant so we only need to look at differentiating x^2 by use of the power rule.
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
When we get done, we will plug in the bottom, the top, the derivative of the bottom, and the derivative of the top into the following formula I gave you earlier: \[y'=\frac{ (\text{ derivative of top }) \cdot (\text{ bottom } )  ( \text{ derivative of bottom } ) \cdot ( \text{ top } )}{(bottom)^2} \]
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
So so far we have: \[y'=\frac{ (\text{ derivative of top }) \cdot (x^24a^2)  ( \text{ derivative of bottom } ) \cdot ( a(xa)^2 )}{(x^24a^2)^2} \]
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
I'm just asking you now to give me the derivative of \[ (a(xa))^2 \text{ and } (x^24a^2) \].
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
For (a(xa))^2, it would be 2x2a. For (x^24a^2), it would be 2x.
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
For the first one, couldn't you just leave it as 2(xa) but don't forget to bring down that a in front. :) So you would actually have what for the first one?
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
Would it be 2a(xa)? :O
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
Yep so we have \[y'=\frac{ (\text{ derivative of top }) \cdot (x^24a^2)  ( \text{ derivative of bottom } ) \cdot ( a(xa)^2 )}{(x^24a^2)^2} \] = \[y'=\frac{ ( 2a(xa) ) \cdot (x^24a^2)  ( 2x ) \cdot ( a(xa)^2 )}{(x^24a^2)^2}\] = \[=\frac{2a(xa)(x^24a^2)2xa(xa)^2}{(x^24a^2)^2}\]
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
Now what factors in the numerator do the two terms on top have in common?
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
Yes. :) So factor that out.
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
\[2a(xa)(x^24a^2)2xa(xa)^2\] = \[2a(xa)[ ?  ?]\]
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
2a(xa){(x^24a^2)x(xa)}
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
Yep You will have \[\frac{2a(xa)[(x^24a^2)x(xa)]}{(x^24a^2)^2}\] You can simplify what you have in brackets above though.
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
\[\frac{2a(xa)(x^24a^2x^2+xa)}{(x^24a^2)^2}\] You have like terms. :)
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
Do you see the like terms to combine?
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
Yep. I'll end up with 2a(xa)(xa4a^2). Right?
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
Ok great now set equal factor equal to zero You are almost there :)
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
a is a positive constant so 2a can never be zero so set xa equal to zero and set xa4a^2=0 Solve both for x to find the critical numbers :)
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
So I'll have x=a and x=4a? What do I do now?
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
It said find the coordinates so find what y is if x=a and find what y is if x=4a
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
If x=a, then y=0. If x=4a, y=9a^3. Is it correct?
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
No. Sorry. For x=4a, y is undefined.
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
Your first one is right. Your second one is wrong.
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
So y is not undefined?
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
Oops. I found out my mistake. For x=4a, y=3a/4. Thank you soooooo muchhhhh @myininaya ! :D
 one year ago

emcrazy14Best ResponseYou've already chosen the best response.0
One more thing, how do I show which is the minimum point and which is maximum? Is it by the second derivative?
 one year ago
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