How do you work out where the peak on a graph should go?

To determine the peak on a graph, you first analyze the function or data set to identify critical points where the derivative equals zero, indicating potential maxima or minima. You can then use the second derivative test to confirm if these points are indeed peaks. Additionally, examining the surrounding values helps to confirm that the identified point is higher than its neighbors, establishing it as the peak. Visualization tools, like graphing software, can also aid in quickly identifying peaks in data sets.