What is the Gradient function?

Question

Paisley Johnson · Accepted Answer

A straightforward method for determining a function's slope at any given point is to use the gradient function.

For a straight line graph, the slope can usually be found very easily by dividing the "rise" by the "run" (i.e., the amount a function goes "up" or "down" over a certain interval). The process for a curved line is quite similar: choose an interval and figure out how much "rise" or "fall" the graph experiences over this interval. The interval should be fairly small, though, or we risk getting some rather odd values!

Consider the function of sin(x), for example. We are aware that

If we were to calculate rise/run in this case, we'd get #(0-0)/(pi-0)#, giving us a slope of 0. But we know that's not the case, because the graph of sin(x) behaves very differently! So we need to make the interval as small as possible in order to make the gradient function work for us.

Emilia Aguilar · Answer

undefined The gradient function, also known as the derivative, measures the rate of change of a function at any given point. It calculates the slope of the tangent line to the graph of the function at that point. The gradient function is a fundamental concept in calculus and is used to analyze the behavior of functions, find maximum and minimum points, and solve optimization problems.