Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be:
f(x) = sinx − cos x, 0 < x < 2π
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Solution
f(x) = sin x − cos x, 0 < x < 2π
∴ f'x = cosx+sinx
f'x=0⇒cosx=-sinx⇒tanx=-1⇒x=3π4,7π4∈0,2π
f''x=-sinx+cosx
f''3π4=-sin3π4+cos3π4=-12-12=-2<0
f''7π4=-sin7π4+cos7π4=12+12=2>0
Concept: Maxima and Minima
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