The same definition is applied to the tangent plane; tangent plane to a surface at a given point is the plane that just touches the surfaces at that point.
Let a function y = f (x) then the Slope of the tangent is the gradient of the function i.e. dy / dx. Then the equation of the tangent line (L, M) is given by:
y – M = dy / dx ( L ) . (x - L)
Where ( x, y) denotes the coordinates of any point on the tangent line. The tangent line’s equation can be determined by the use of polynomial division to divide ∫ f(x) by ( x – L )2 if the remainder is denoted by the function g(x) then the equation of the tangent line is given by:
y = g( x)
When the equation of the curve having two variables and denoted by f(x, y) = 0 then the slope of the function is given by:
dy / dx = - ( δf / δx) / ( δf / δy ),
Then the expression for the tangent function or tangent line is given by:
( δf/ δx ) (L, M). (x - L) + ( δf / δy )(L , M) . ( y - M) = 0.