Newton's Method Question (1 Viewer)

[cutemouse]

Hi, Could someone please help me with parts (iii) and (iv) of this question? Thanks

Consider the polynomial P(x)=2x³-3x²-7
i) Prove there is at least one real root in the interval 2<x<3 DONE

ii) Use Newton's method with two applications to estimate the root of P(x)=0 correct to 2 decimal places by taking x=2.3 as a first approximate. DONE:
z³=2.21 (to 2 dp)

iii) Comment on the accuracy of your answer in (ii) (1 mark)

iv) Why would 2.1 have been a worse choice as a first approximation? Include a detailed diagram with your answer. (2 marks)

Thanks

 

[Scinery]

newtons method does not account for stationary points, because there will in that case be no x intercept. you could also end up on the wrong side of the curve..

 

[youngminii]

If you draw the curve, you'll see that it rises very quickly around the the intercept (starts rising at 1.5 very quickly and then starts rising steadily at around 2.2 - 2.3) which mucks up Newton's Method.

 

[cutemouse]

Hmm I don't think that x=2.1 isn a stat pt.

How would you sketch P(x)=2x³-3x²-7?

Thanks

 

[youngminii]

Hmm I don't think that x=2.1 isn a stat pt.

How would you sketch P(x)=2x³-3x²-7?

Thanks

Lol I used a curve sketcher (I'm lazy)
There's a stat point at (1, -8) and (0, -7).
The exact root is x = 2.214015..