Suppose 
is the equation of any curve.
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So here are the first two formulas.
EQUATIONS OF THE TANGENT AND THE NORMAL TO ANY CURVE
The equation of the tangent of this curve at the point 
is
Similarly, the equation of the normal to this curve at the point is
Now comes two more formulas.
EQUATION THE RADIUS OF CURVATURE OF ANY CURVE
Now the equation of the radius of curvature 
at any point is
![\[R=\frac{\left[1+\left(\cfrac{dy}{dx}\right)^2\right]^{3/2}}{\cfrac{d^2y}{dx^2}}.\]](https://appassets.softecksblog.in/engineering_mathematics/assets/em2/3_files/image006.webp)
EQUATION OF THE CENTER OF CURVATURE OF ANY CURVE
The equation of the center of curvature 
at any point is
MAXIMUM AND MINIMUM VALUES OF FUNCTIONS
Let’s say is a function.
For any maximum or minimum value of 
.
For the minimum value of 
, the value of 
.
POINTS OF INFLEXION
Let’s say is a function.
For the point of inflexion, 
. Also, there will be a change of sign at 
when it passes through the point.
