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In book it is written that $\sin(x)$ has both local maximum and global maximum 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?

Peter Phipps
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Khan Saab
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  • A 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. – k99731 Jan 22 '17 at 14:13
  • is the global maximum not unique? – Khan Saab Jan 22 '17 at 14:17
  • It does not have to be unique. It just has to be greater than or equal to all other values. – k99731 Jan 22 '17 at 14:18

1 Answers1

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A global maximum is always a local maximum but the inverse doesn't always happen to be true.

Varazda
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