The equation of tangent and normal line to a curve of a function can be calculated by using the derivatives. If we have a curve of a function and we want to find the equation of the tangent to a curve at a given point, then by using the derivative, we can find the slope and equation of the tangent line. A tangent is a line to a curve that will only touch the curve at a single point and its slope is equal to the derivative of the curve at that point. The slope(m) of the tangent to a curve of a function y = f(x) at a point (x1,y1)(x1,y1) is obtained by taking the derivative of the function (m = f'(x) ).
By finding the slope of the tangent line to the curve and using the equation m=(y−y1)/(x−x1)m=(y−y1)/(x−x1), we can find the equation of the tangent line to the curve. Similarly, we can find the equation of the normal line to the curve of a function at a point. This normal line will be normal(perpendicular) to the tangent line. Hence the slope of the normal line to a curve of a function y = f(x) at a point (x1,y1)(x1,y1) is given as follows.
n = -1/m = – 1/ f'(x)
And by using the equation
−1/m = (y−y1) / (x−x1)−1/m = (y−y1)/(x−x1)
we can find the equation of the normal line to the curve.
