TopTangent line or Straight Line to a plane curve at a given Point is the line that touches the curve at that point. Tangent of a function is an angle measured in radians. It’s a Tangent to a curve y = f(x) at a point a on the curve with the satisfied condition that line passes through the point (a, f (a)) present on the curve and have the Slope f’(a). Here f’ (a) is the first derivative of the function at point a.
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.