Math Is Fun Forum

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Slope of a Normal?

Find the slope of the normal to y= 2x²-2 at the point x=-4.

Uh... what's a normal?

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Slope of a Normal?

the normal to a curve/surface is a line perpendicular to it and passing through the point chosen (as opposed to a tangent which is parellel)

so, y = 2x²-2, dy/dx = 4x, (x = -4) dy/dx = -16

now, you should know from geometry of straight lines, that two lines are perpendicular, when the product of their gradients is -1

so -1 / -16 = 1/16, and that is the gradient of the normal.

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George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Slope of a Normal?

Or just imagine y=2x[sup]2[/sup]-2 is a special case of g(x,y)=y-2x[sup]2[/sup]+2=0
find
(g'[sub]x[/sub],g'[sub]y[/sub]) at the given point (x,y)=(-4,30)

Last edited by George,Y (2007-01-26 16:54:33)

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X'(y-Xβ)=0