# Relative extrema and absolute extrema with only one relative extrema in the function

If a relative maximum is the only relative extrema for it's function, and the function is continuous, can it be guaranteed to be the absolute maximum of the function? And a relative minimum which is the only relative extrema would be the absolute minimum? If so, is there any law that states this?

• Look at the graph of $f(x)=x^2(x-1)$ – John Wayland Bales Sep 17 '17 at 23:54
• @JohnWaylandBales did you mean $f(x) = (x^2)(x-1)$? Or $f(x) = x^(2(x-1))$? – Jamman00 Sep 18 '17 at 0:10
• The expressions $f(x)=x^2(x-1)$ and $f(x)=(x^2)(x-1)$ are equivalent. – John Wayland Bales Sep 18 '17 at 0:13
• There are 2 relative extrema for the function $f(x) = x^2(x-1)$ – Jamman00 Sep 18 '17 at 0:33
• Sorry, I misread your question as "If a relative maximum is the only relative maximum $\cdots$". – John Wayland Bales Sep 18 '17 at 0:37

$$f(x)=\frac{|x|(x-1)}{x^3}$$