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# A-Level Differentiation Part 2

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1. Stuck again.

Question:
The maximum point on the curve with the equation y=xsin^0.5x where 0<x<pi is A. Show that the x coordinate of A satisfies the equation 2tanx+x=0.

I've differentiated it to sin^0.5x +xcosx/2sin^0.5x, but cant work out how to get the maximum point.
2. set the differential equal to zero, take out sinx as a common factor
3. (Original post by LukeMontgomery)
Stuck again.

Question:
The maximum point on the curve with the equation y=xsin^0.5x where 0<x<pi is A. Show that the x coordinate of A satisfies the equation 2tanx+x=0.

I've differentiated it to sin^0.5x +xcosx/2sin^0.5x, but cant work out how to get the maximum point.
set **sin^0.5x +xcosx/2sin^0.5x to zero

multiply each term by *sin^0.5x

to get tanx you need to think of sinx/cosx ....*
4. (Original post by the bear)
set **sin^0.5x +xcosx/2sin^0.5x to zero

multiply each term by *sin^0.5x

to get tanx you need to think of sinx/cosx ....*
If I times both sides by sin^0.5x then I get sinx+xcosx/2=0

What do I do from there?
5. (Original post by LukeMontgomery)
If I times both sides by sin^0.5x then I get sinx+xcosx/2=0

What do I do from there?
you need to somehow get tanx to appear.... *
6. (Original post by the bear)
you need to somehow get tanx to appear.... *
sinx+xcosx/2=0

2sinx+xcosx=0

2sinx/cosx+xcosx/cosx=0

=2tanx+x=0

Ok so I've done that, but how do I work out the x coordinate of A.
7. (Original post by LukeMontgomery)
sinx+xcosx/2=0

2sinx+xcosx=0

2sinx/cosx+xcosx/cosx=0

=2tanx+x=0

Ok so I've done that, but how do I work out the x coordinate of A.
You don't have to. It simply asks you to show that it satisfies that equation and you've done it. It's a transcendental equation anyhow so you cannot solve it using analytical methods, unless you say x=0 but that's not the only solution.
8. (Original post by RDKGames)
You don't have to. It simply asks you to show that it satisfies that equation and you've done it. It's a transcendental equation anyhow so you cannot solve it using analytical methods, unless you say x=0 but that's not the only solution.
Ok good, thanks!
9. you could use something like the Newton-Raphson method to solve it after that.

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