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dooder:
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?

Freitag:

--- Quote from: "dooder" ---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?
--- End quote ---


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.

Freitag:
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.

Jasper:

--- Quote from: "Freitag" ---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.
--- End quote ---


Can someone confirm this? I thought you can't use f''(x) in methods.

Fitness:

--- Quote from: "Jasper" ---
--- Quote from: "Freitag" ---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.
--- End quote ---


Can someone confirm this? I thought you can't use f''(x) in methods.
--- End quote ---


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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