In book it is written that sin(x) has both local max and global max at $\pi/2$ but the highest value sin can have is $1$ and that is at $\pi/2$. Should not it be only global maximum?
Local max and global max of sin
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$\begingroup$
maxima-minima
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0A point can be global maximum and local maximum at the same time. Remember in the definitions of local maximum and global maximum, it is possible for a point to be both of them. – 2017-01-22
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0is the global maximum not unique? – 2017-01-22
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0It does not have to be unique. It just has to be greater than or **equal to** all other values. – 2017-01-22
1 Answers
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A global maximum is always a local maximum but the inverse doesn't always happen to be true.