I have read that Gradient of a scalar function points in the direction in which the function is the highest. But, according to another source, the gradient function is normal to the surface of the function, I don’t get which one it is? How can I understand the gradient function? I think of it as a 3D slope of a function at a point, but I don’t know how to incorporate that with normal to the surface!
In: 1
Where did you read the bit about it being normal to the surface? Gradient vectors point in the direction of greatest increase.
When I answer math questions I usually go being the scope of “explain like I’m *five*” because it’s usually for someone’s course understanding, so here’s the “explain like I’m taking a course on this” explanation:
It’s analogous to regular 1D functions f(x). If f is increasing, df/dx is positive. If you think of a number as a 1D “vector”, then a positive number points towards the right, which is the direction in which changing x causes f(x) to increase. Likewise if the derivative is negative, then you have to move x to the left to cause f(x) to increase. When you start adding more dimensions to your input, the gradient vector will point in the direction in which changing the inputs will cause the greatest increase in the value of f
Latest Answers