How do you determine whether the function f(x)=sin⁡x−cos⁡x is concave up or concave down and its intervals?

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webhui2v2 · Accepted Answer

Step 1f(x)=sin⁡x−cos⁡xf′(x)=cos⁡x+sin⁡xfx)=−sin⁡x+cos⁡xfx)=0 where sin⁡x=cos⁡x or tan⁡x=1This happens at x=π4+πk for integer k.For π4&amp;lt;x&amp;lt;5π4 we have sin⁡x&amp;gt;cos⁡x so fx)&amp;lt;0 and the graph of f is concave down.For −5π4&amp;lt;x&amp;lt;π4 we have sin⁡x&amp;lt;cos⁡x so fx)&amp;gt;0 and the graph of f is concave up.Step 2Both sine and cosine are periodic with period 2π, soon intervals of the form (π4+2πk,5π4+2πk), where k is an integer, the graph of f is concave down.on intervals of the form (−5π4+2πk,π4+2πk), where k is an integer, the graph of f is concave up.There are, of course other ways to write the intervals.

How do you determine whether the function

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