ATAR Notes: Forum
VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: dooder on November 11, 2007, 08:35:23 pm
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Is this correct:
To prove a certain point is certain type of stationary point you must take f'(x) just to the left and right of it (or f(x))
However to find what type it is it is sufficient to use f''(x)
Or can either method be used interchangably (just concerned about this find/prove stuff)
Also: if f''(x) = 0, does that mean it is a point of inflection?
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Is this correct:
To prove a certain point is certain type of stationary point you must take f'(x) just to the left and right of it (or f(x))
However to find what type it is it is sufficient to use f''(x)
Or can either method be used interchangably (just concerned about this find/prove stuff)
Also: if f''(x) = 0, does that mean it is a point of inflection?
You are taught f''(x) = 0 as a P.O.I in specialist, not methods, so I don't think you'll get any marks awarded for using that.
The best way to prove what sort of stationary point you're dealing with is to find the stationary point, and check whether the gradient is negative or positive on either side of the point.
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Wait, I speak a lie. I saw it in a textbook once. Nevermind my message. I believe it's acceptable to examine the sign of f''(x) and use it to comment on the type of stationary point.
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Wait, I speak a lie. I saw it in a textbook once. Nevermind my message. I believe it's acceptable to examine the sign of f''(x) and use it to comment on the type of stationary point.
Can someone confirm this? I thought you can't use f''(x) in methods.
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Wait, I speak a lie. I saw it in a textbook once. Nevermind my message. I believe it's acceptable to examine the sign of f''(x) and use it to comment on the type of stationary point.
Can someone confirm this? I thought you can't use f''(x) in methods.
Well you don't learn sec, cosec and cot in methods but those answers are acceptable. And it is mathematically correct ...
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You can do it either way, i suppose.
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Also: if f''(x) = 0, does that mean it is a point of inflection?
POI's are points of curvature changes. It is necessary but not sufficient that f''- = 0. You also require that the sign of the second derivative changes. For example, graph goes from concave up to concave down or vice versa.
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Also: if f''(x) = 0, does that mean it is a point of inflection?
POI's are points of curvature changes. It is necessary but not sufficient that f''- = 0. You also require that the sign of the second derivative changes. For example, graph goes from concave up to concave down or vice versa.
In other words, it must cross the x-axis. f''(x) = 12x^2 for example, has f''(x) = 0 at x = 0, but it is a turning point (doesn't cross the x-axis), so there is no point of inflection for f(x) = x^4
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i would check a value of f'(x) before and after f'(x)=0 and if the gradents are positive and negative or visa versa then that proved
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There is more about this here:
http://freestudynotes.com/VCEforum/viewtopic.php?t=217&start=15
I don't think it's required for methods though.