Applications Of Derivatives – Tangents and Normal

The derivative of a function y

The derivative of a function y = f(x) at a point (x₁, y₁) gives the slope of the tangent line at that point. The slope of the normal line is the negat

Using the point

Using the point-slope form of a line, the equation of the tangent is y − y₁ = f'(x₁)(x − x₁), and the equation of the normal is y − y₁ = −1/f'(x₁)(x −

These are geometric lengths associated

These are geometric lengths associated with the tangent and normal lines. For a point (x, y) on a curve, the lengths are calculated using the derivati

Rolle's Theorem states that if

Rolle's Theorem states that if a function is continuous on [a,b], differentiable on (a,b), and f(a) = f(b), then there exists at least one point c in