Differential Calculus -The Equation of Tangent and Normal to a Curve

Differential Calculus:

The Equation of Tangent and Normal to a Curve problems and step-by step solutions.

Students think critically, demonstrate knowledge of functions and differential calculus.

• Apply the appropriate formulas, sketch the graph of y = f(x) with the tangent and normal.
• Use mathematical strategies to solve all questions.

Learning Outcomes:

• Understand the derivative as the gradient of the tangent to the curve of y = f(x) at a point.
• Understand that the normal on the curve is perpendicular to the tangent.
• Find the gradient of the tangent and normal at a point on the curve.
• Find the equation of the tangent and normal of the curve at a point.
• Practise sketching a curve with the tangent and normal.
• Find the angle of inclination.

Grades: 11th to 12th

Comply with Australian Curriculum

• Interpret the derivative as the gradient of the tangent to the graph of y = f(x) at a point (ACMMM085)
• Estimate numerically the value of the derivative at a point, for simple power functions (ACMMM086)
• understand the concept of the derivative as a function (ACMMM089)

Differential Calculus Resources:

Differential Calculus -The Equation of Tangents to a Curve- Critical Thinking

Differential Calculus -The Equation of Tangent and Normal to a Curve