C3 Trig/Differentiation / Integration / Weird Question.

There's one question I'm really stuck on, I don't get any of the parts. Here it is:

A curve has equation y = (2x - 1)tan2x, 0< x < π/4

The curve has a minimum point P. The x-coordinate of P is k.

a) Show that k satisfies the equation

4k + sin4k - 2 = 0

(I assume you have to differentiate the equation, and then make it equal to 0 as it is a stationary point but I have no idea how to get from that to this)

b) The iterative formula x(n + 1) = 1/4(2 - sin4x(n)), x(0) = 0.3

is used to find an approximate value for k. Calculate the values of x(1), x(2), x(3) and x(4) to 4 d.p.

(I managed to do this part)

c) Show that k = 0.277 to 3 s.f.

(I found f(0.2765) and f(0.2775) and surely there should be a change of sign to show k = 0.277 is correct, but they were both negative so this can't be right?)

Does anyone know how to get started on this question? Particularly part a)?
Thankyou.

Reply 1

yusufu

16

what do you get when you differentiate the function for a)?

Reply 2

The Muon

2

Joy:):)

There's one question I'm really stuck on, I don't get any of the parts. Here it is:

A curve has equation y = (2x - 1)tan2x, 0< x < π/4

The curve has a minimum point P. The x-coordinate of P is k.

a) Show that k satisfies the equation

4k + sin4k - 2 = 0

(I assume you have to differentiate the equation, and then make it equal to 0 as it is a stationary point but I have no idea how to get from that to this)

b) The iterative formula x(n + 1) = 1/4(2 - sin4x(n)), x(0) = 0.3

is used to find an approximate value for k. Calculate the values of x(1), x(2), x(3) and x(4) to 4 d.p.

(I managed to do this part)

c) Show that k = 0.277 to 3 s.f.

(I found f(0.2765) and f(0.2775) and surely there should be a change of sign to show k = 0.277 is correct, but they were both negative so this can't be right?)

Does anyone know how to get started on this question? Particularly part a)?
Thankyou.

For part a you have to differentiate using the product rule and then let that = 0. Then it takes ome rearranging to get to what you need. First think you will need to do is change you sec^2(2x) to a 1/(cos^2(2x)) and also your tan(x) into sin/cos. Then when you multiply by cos^2 you see something which resemble the double angle formulae for sin 4x instead of sin 2x

remember that sin4x = 2sin2xcos2x