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Is it possible to predict if a single variable function of form y= f(x) can have a point with zero slope without plotting an X-Y graph of the function??

Also if a function of form y=f(x) have points with zero slopes, is it possible to predict if one of these points represent the maximum of that function, without plotting an X-Y graph of the function ??

Saasmspslse Ueseer
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    If it is continuous on $[a,b]$, differentiable on $(a,b)$ and $f(a)=f(b)$ then it will have points with zero slope on $(a,b)$ by the Mean Value theorem, and at least one of them will be a min or a max. – Conifold Dec 31 '19 at 04:10
  • If the function is differentiable, yes; find the derivative and solve $f’(x)=0$; then use the first derivative test to check if they are extremes. – Arturo Magidin Dec 31 '19 at 04:10

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