How can the highest and lowest point be determined?

Answer 1

In a graph, you can use differential calculus to calculate the values of the highs and lows. You can eyeball them too. Say the equation of the curve is y = x^2 + x + 1. y' = 2x + 1. The max and min will occur at y' = 0, where x = -0.5. From visual, it happens at a min. The coordinates of the min are (-0.5, 0.75).

In Excel, use the max(cell range) or min(cell range) function to determine the min and max values.

In the real world, you can use a level to tell the horizon, then use an instrument to measure the angle from your location to the highs and lows, with respect to the horizontal reference. A positive angle means 'up' -- you are looking at a high. A negative angle means 'down' -- you are looking at a low. The angle-measuring instrument can be a quadrant or an inclinometer. Then you need to measure the distance on the horizon of the projection of the high or low to your location. For a building, the projection will be the front entrance door, for example. For a tree, the bottom of the trunk. For a mountain, that would require a laser ranging tool.

Answer 2

The highest point can be determined by identifying the peak elevation, while the lowest point can be determined by identifying the lowest elevation. This information is typically obtained through topographic maps or by using digital elevation models and geographic information systems.