Calculus Differentiation - The Gradient and Equation of a Tangent to a Curve
- Zip
Description
Introduction to Differentiation
Students’ printable book contains cover, scaffolded notes (blank and complete notes) and 4-worksheets to
- learn and practise finding gradients and the equation for tangents to curves.
- practise sketching the graphs of y = f(x) and their tangents.
- recognise that the tangent line at a vertex of the curve is a horizontal line.
2 Styles of student book:
- Student Book Style 1 (Cover + Blank Notes + Worksheets)
Teacher and students work together to complete the question in the examples.
- Student Book Style 2 (Cover + Complete Notes + Worksheets)
Use book style 2 if you prefer complete notes as a teaching aid.
Total pages in each book: 15 pages
Printable for transparencies and whiteboards, answer keys and note booklet are also included.
Skill level: Beginner (Easy)
Grades: 11th to 12th
Key learning:
- Define the derivative f’(x) from first principles, as a limit h→0 where y = f(x).
- Use first principles to find the derivative of simple polynomials, up to degree 2.
- Interpret the derivative as the gradient of the tangent to the graph of y = f(x) at a point.
- Find the derivative of f(x) = mx + b.
- Find the gradients of the tangents to y = ax^2 + c and y = ax^2 + bx + c at a point on the curve.
- Find the equation of the tangent to the curve at a point.
- Understand that the tangent line at a vertex is a horizontal line.
- Practise to sketch the curves and the tangents.
THIS RESOURCE INCLUDES: 6 pdf files in one zip.
File 1: Resource Description
File 2: For Transparencies and Whiteboards (Blanks and Complete Notes)
File 3: Book Style 1 (Cover + Blank Notes + Worksheets) (18 pages)
File 4: Book Style 2 (Cover + Complete Notes + Worksheets) (18 pages)
File 5: Answer Keys (14 pages)
File 6: Notes Booklet (3 pages)
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)
Related resources:
Calculus Differentiation - The Derivative fʹ(x) as A Limit - First-Principles Differentiation
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