Episode 6 — Differential Calculus

Equations of tangents to graphs

Learners will be able to:

• Identify the concept of a tangent to a curve as a straight line that touches the curve at a point. • Explain why the gradient of a tangent to a curve is equal to the derivative of the function at the point of contact. • Calculate the gradient of the tangent to a curve by substituting the x-value into the derivative function. • Find the equation of the tangent to a curve using the gradient and a point on the curve. • Solve for the coordinates of a point where the gradient of the tangent to a function is equal to a given value.