Describe how you would find the maximum and minimum values for tangent of the typical angles used on the unit circle. what are these values?

3down votefavorite1Find minimum and maximum value of function f(x,y)=3x+4y+|x−y| on circle{(x,y):x2+y2=1}I used polar coordinate system. So I have x=cost and y=sint where t∈[0,2π).Then i exploited definition of absolute function and i got:h(t)={4cost+3sintt∈[0,π4]∪[54π,2π)2cost+5sintt∈(π4,54π)Hence i received following critical points (earlier i computed first derivative):cost=±45∨cost=±2√29Then i computed second derivative and after all i received that in (2√29,5√29) is maximum equal √29 and in (−45,−35) is minimum equal −235

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