Tangent and Normal Lines of Curves:

From the given definitions; f '(x) is the slope of the tangent line of a curve at a certain point. From the point slope formula, the formula for the tangent line of a curve at a given point is:

y - y₀ = f '(x₀)(x - x₀)

The normal line is the line that is perpendicular to the tangent line of a curve. The formula for normal lines is:

y - y₀ = 1/ f '(x₀)(x - x₀)

(Recall that the product of the slope of perpendicular lines is -1: m₁ m₂ = -1)

If the function f is differentiable at x , then f is continuos.