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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: DrDin213 on November 07, 2018, 05:06:35 pm

Title: Justifying if a turning point is a minimum or maximum
Post by: DrDin213 on November 07, 2018, 05:06:35 pm

Hi.
If we are given a problem where we need to minimise or maximise something, do we have to verify the nature of the stationary point even if the question doesn't ask?

Title: Re: Justifying if a turning point is a minimum or maximum
Post by: S_R_K on November 07, 2018, 05:38:05 pm

Quote from: DrDin213 on November 07, 2018, 05:06:35 pm

Hi.
If we are given a problem where we need to minimise or maximise something, do we have to verify the nature of the stationary point even if the question doesn't ask?

Assuming that the domain is closed (ie. includes its endpoints) then the max / min will occur at either an endpoint or stationary point, so checking the values of each of these is sufficient. So, no, there's no need to do a sign diagram or first-derivative test, if the question doesn't give specific instructions.