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anonymous
 one year ago
Need Help! Find where the function f(x)=x+sqrt(1x) is increasing and decreasing.
anonymous
 one year ago
Need Help! Find where the function f(x)=x+sqrt(1x) is increasing and decreasing.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439260678254:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0step one find the derivative

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439260757824:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let me know when you get \[f'(x)=1\frac{1}{2\sqrt{1x}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm just having trouble trying to solve for x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok lets back up a second

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0exponential notation is great for computing certain derivatives, but it totally sucks for doing actual numeric computation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the square root function is a very very very common function so you should commit its derivative to memory and not screw around with rational exponents \[\frac{d}{dx}[\sqrt{x}]=\frac{1}{2\sqrt{x}}\] like memorizing \(6\times 9=54\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and via the chain rule \[\frac{d}{dx}[\sqrt{f(x)}]=\frac{f'(x)}{2\sqrt{f(x)}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I didnt learn it that way, I was taught to set it up with the 1/2 in the front and 1/2 as the exponent value. But if doing it the way above helps me solve the problem, ill stick with it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0math teachers love to put the square root function on a test, quiz etc so while your colleages are converting to exponents, then using the power rule etc, you should go right to \[f'(x)=1\frac{1}{\sqrt{1x}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah the power rule works for sure, but the derivative never changes

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so once you know it, you know it like \(8\times 7=56\) it is always the same and yes, you need to do any computation at all with a derivative, you have to get rid of the rational exponent and write what it actually is

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439261266064:dwSo would the function look like this

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now you can solve \[1\frac{1}{2\sqrt{1x}}=0\] to find the critical points etc you cannot do it with \[1\frac{1}{2}(1x)^{\frac{1}{2}}\]that form i useless

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah what you wrote now we can do it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do we multiple the 1 by the denominator of the other fraction?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you want to set it equal to zero and solve probably a good first step

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0notice that the deriviative has domain \(x<1\) which is not surprising because the original function has domain \(x\leq 1\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0also notice that the derivative is strictly decreasing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So does x equal 3/4 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which means all that is left to do is solve \[1\frac{1}{2\sqrt{x1}}=0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so then I would make a number line and test points on the left and the right and see where it is postive and negative which should give me where the function is inc or dec?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so \(f'(x)<0\) i.e is negative if \(x\geq \frac{3}{4}\) and \(f'(x)>0\) i.e positive of \(x\leq\frac{3}{4}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah you can do that if it is not obvious

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then translate to increasing decreasing for \(f\) and you are done

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0quick quiz \[\frac{d}{dx}[\sqrt{1x^2}]=?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so (infinity, 3/4) is incr and decreasing from (3/4, infinity)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh no hold the phone

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0increasing on \((\infty, \frac{3}{4})\) is right

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01/(2*sqrt(1x^2))*2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0close the numerator should be \(2x\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and of course the two's cancel

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh yea, was in a rush

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok lets get back to your question

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f(x)=x+\sqrt{1x}\]right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it undefined from 3/4 to infinity

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0don't write that is increasing on \((\frac{3}{4},\infty)\) or your teacher will think you are daft

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the domain is \[(\infty, 1]\] right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right so we just dont include the 3/4 to infinity part, right?!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so it is only increasing on \[(\frac{3}{4},1)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah you include it , but dont to to infinity

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0three fourth is less than one, so there is an interval over which it increases

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and that's because of the domain that you were explaining before

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oops is said "increase" i meant "decrease"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok want to see a picture?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=x%2Bsqrt%281x%29 click on "real valued plot" otherwise you will get complex plot which is not what you want

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yw \[\frac{d}{dx}[\sqrt{x^2+2x1}]=?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01/(2*sqrt(x^2+2x1) * 2x+2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right, better knows as \[\frac{x+1}{\sqrt{x^2+2x1}}\] easy right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so no more screwing around with rational exponents when dealing with square roots!!
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