Hi I am having trouble understanding how the gradient of a scalar field is the direction along the xy plane that yields the maximum inclination. Sure it takes into account the partial derivatives along both the x and y axes but does that mean "maximum inclination"? How do the partial derivatives come into the gradient vector field?
A basic intuition would be great.
Sorry for phrasing the question badly...I am a high school student venturing on some multivariate calculus so please bear with me.
Thank You in advance.