why is direction of gradient vector steepest?

Question

anonymous · Answer

....erm..can you make your question a bit clearer?

m · Answer

steepest derivative, it says walk in the direction of gradient vector

anonymous · Answer

whats the equation given

m · Answer

just the general directional vector
|U||del(f)}cos(theta)

m · Answer

Duf

m · Answer

gradient represents the steepest rate of increase of some function for each of the points where the function is defined, but each gradient vector is also perpendicular to the level tangent directions at a point. Note that these gradient vectors are not "normal" to the surface of the hill - as in pointing up into the sky. They are normal to level directions.

anonymous · Answer

The dell is always unitized, that means it is always positive, it is related to the slope, derivative, positve slope.

m · Answer

why is gradient vector the steepest ascent?

anonymous · Answer

It has a relation to the cos function which is merely between 1 and -1. It always end on the +1 side.

m · Answer

and max is when cos = 1?

anonymous · Answer

Yeah, in fact the magnitude of unit vector is equal to 1 so it always win out.

m · Answer

thanks