find relative maximum in graph function

Question

Find relative maximum in the graph above

For me, the answers are zero and two, but according to the correctness of the exam, the answer is incorrect

Answer 1

Local maxima $x$ of a function $f$ are points such that $f(x)\geq f(y)$ for all $y\in(x-\varepsilon,x+\varepsilon)$. You can modify the definition a little bit to fit at the ends of the interval.

You correctly identified $x=0$ and $x=2$. In addition to those, $x=5$ is a local maximum since $f(5)\geq f(y)$ for all $y\in (5-\varepsilon,5]$.