Question

What is a gradient?

Answer 1

depends on context

Answer 2

calculus. Tells me to find the gradient of a normal

Answer 3

the gradient is the then the partial derivatives of a surface equation

Answer 4

the gradient in effect creates equations for the normal of the surface at any given point

Answer 5

the gradient points in the direction of the greatest increase as well

Answer 6

um...does this by chance deal with perpendicular lines?

Answer 7

lol, it would be nice to have a whole question to work with instead of trying to piece one together

Answer 8

The gradient of a scalar field (written \( \nabla f\)) is the partial derivative of the f with respect to x, of the function with respect to y and so on. \[ \nabla f = (\frac{\partial f}{ \partial x}, \frac{\partial f}{ \partial y}, \frac{\partial f}{ \partial z}) \]As @amistre64 pointed out, it gives the direction of the greatest increase, etc. Also, the grad is a vector.

Answer 9

almost thought bmp got trapped in the vortex of the damned ...

Answer 10

Haha, I forgot the latex for partial. Had to look for it. I was trying \der and stuff like that :-)

Answer 11

\nabla i think

Answer 12

Hm...this question is weird. Ill give you an example
So it says find the gradient of the normal to the curve: x^2 +3x +4 at the point x=5

Answer 13

For partial it's only \partial. I was trying the hard way :-)

Answer 14

So basically, it tell you to take the derivative and solve at that point, and then you take the negative reciprocal at the end?

Answer 15

ah, then that means the slope of the line that is perp to the tangent at x=5

Answer 16

Yup, do that @bobobobobb :-)

Answer 17

-1/(dy/dx) should suffice

Answer 18

ohhh. gradient of the normal means perpendicular?

Answer 19

the normal is perp to the tangent; so yes

Answer 20

i think they try to tie in the notion of gradient point to highest rate of change and relate it to the slope of a line

Answer 21

in R^2 gradient just refers to slope

Answer 22

I think this always holds for the Euclidean space.