C3 help!!!!

http://pmt.physicsandmathstutor.com/download/Maths/A-level/C3/Papers-Edexcel/January%202007%20QP%20-%20C3%20Edexcel.pdf

For question 7d how do I know the graph is U shaped, exam solutions said its U shaped, but how do I know that. This doesnt look quadratic either.

Thank you

Reply 1

DJB2K

3

Graphs of functions to the fourth degree are u-shaped, and you can see that it is to the fourth power. I think you're just supposed to recognise that it would be U-shaped somewhat

Original post by JustgotAstar

http://pmt.physicsandmathstutor.com/download/Maths/A-level/C3/Papers-Edexcel/January%202007%20QP%20-%20C3%20Edexcel.pdf

For question 7d how do I know the graph is U shaped, exam solutions said its U shaped, but how do I know that. This doesnt look quadratic either.

Thank you

Any even order polynomial will be ultimately 'U' shaped.

Reply 3

NotNotBatman

20

Original post by RDKGames

Any even order polynomial will be ultimately 'U' shaped.

Only if it's biquadratic, right ? So can be expressed in terms of a quadratic.

Original post by NotNotBatman

Only if it's biquadratic, right ? So can be expressed in terms of a quadratic.

Doesn't have to be.

Original post by NotNotBatman

Only if it's biquadratic, right ? So can be expressed in terms of a quadratic.

A very strangely shaped U perhaps (might be closer to a v/w), but a rough U shape nonetheless.

(edited 6 years ago)

Reply 6

B_9710

18

You have to use he fact that it has one turning point and the fact that it is a polynomial of even degree - which shows

f(x)\rightarrow \infty

as

x\rightarrow \pm \infty

(as coefficient of x^4 is positive anyway).

Reply 7

NotNotBatman

20

Original post by RDKGames

Doesn't have to be.

Ok.

Original post by _gcx

A very strangely shaped U perhaps (might be closer to a v), but a rough U shape nonetheless.

I was thinking more of the w shaped curves, when the coefficients of each x^n is non zero and there's more than one stationary point.
B9710 has explained it really well.

Reply 8

username2586053

OP

8

So say I have x to the power 6, it would be U shaped? Wouldnt the amount of turning points change at all? Would all even powers have 1 turning point then?

Original post by JustgotAstar

So say I have x to the power 6, it would be U shaped? Wouldnt the amount of turning points change at all? Would all even powers have 1 turning point then?

It is 'ultimately' U shaped, yes, because an even order polynomial goes to infinity as

x \rightarrow \pm \infty

. Anything can happen in between the two stems to infinity, you need further analysis of the stationary points to determine what happens there.

All even powers at at least 1 turning point.

C3 help!!!!

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