# Thread: finding roots in given interval /differentiation

1. ## finding roots in given interval /differentiation

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2. Originally Posted by philyc86
hi there
can anyone point me in the right direction about how to show that the following equation has a root in the interval [1.1 , 1.2]

2x-tanx=0
2x-tan(x) is positive at x=1.1 and negative at x=1.2 and as it is continuous on this interval it has a root in the interval.

CB

3. Originally Posted by philyc86
also ,how do i differentiate (x-1)lnx ,i need to find the 2,3,4,and 5th derivative ,and i get stuck as to wheher to use the product or quotient rules and how to deal with some of the powers

thankyou so much

phil
They are essentially the same thing so use which ever is the more convienient, remember that:

$\frac{f(x)}{g(x)}=f(x) \left( \frac{1}{g(x)}\right)$

and that $\frac{d}{dx}\left(\frac{1}{g(x)}\right)=-\ \frac{g'(x)}{(g(x))^2}$

CB

4. p

5. Originally Posted by philyc86
hi