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

Differential Calculus: The Equation of Tangents 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) and their tangents.
• Use mathematical strategies to solve all questions.

Learning Outcomes:

• Use first principles to find the derivative of simple polynomials.
• Understand the derivative as the gradient of the tangent to the curve of y = f(x) at a point.
• Find the gradient of the tangents at a point on the curve.
• Find the equation of the tangent to the curve at a point.
• Practise sketching a curve and the tangents.

Grades: 10th to 12th

Also suitable for Australian Curriculum
Examine the behaviour of the difference quotient (f(x+h)−f(x))/h as h→0 as an informal introduction to the concept of a limit (ACMMM081)
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)