Differentiation and antidifferentiation of polynomials

Mathematical Methods: Units 1 and 2

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Welcome

Learning objectives

Recap of past learning

The sign of the derivative

Example: Finding intervals of gradients

Example: Sketching a derivative graph from a function

Example 2: Sketching a derivative from a function

Example 3: Sketching a derivative graph from a function

Strictly increasing and decreasing

Strictly increasing and decreasing: A warning

Angle of the gradient of a curve at a point

Example 4: Using m equals tan theta

Example 2: Find the direction using m equals tan theta

Final comments

This video is the next in the series relating to differentiation for the Year 11 Mathematical Methods (Units 1 and 2) course. Having done the ground work relating to "how" to differentiate, I now start to look at why it becomes helpful. Looking at the graphs of the derivative is an important aspect of the course and I take time to cover this in terms of the notation used and how to draw graphs of the derivative function when given the original function. I look at what it means for a function to be strictly increasing and decreasing for two points with some worked examples. Finally I look at how we can find the angle between the tangent at a point of a graph and the x-axis using some basic trigonometry. There are lots of worked examples and I do all I can to ensure this topic is covered in an easy to understand way. I cannot stress enough how important this video is!

LEGAL STUFF (VCAA)

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