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Presentation transcript:

Bell-Ringer

Topic 7 – Introduction to Differential Calculus Chapter 20: Differential Calculus Chapter 21: Applications of Differential Calculus

Differential Calculus Chapter 20

Rates of Change A rate is a comparison between two quantities of different kinds. Calculate the rate using the slope formula: m= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1

To find the average rate of change between two points, find the gradient of the line segment between them. Example 2:

To find the instantaneous rate of change (rate of change in a particular instance), find the gradient of the tangent to the graph at that point. Calculate the instantaneous rate of change using the given point and by plugging in (x+h) for x. Example:

The Derivative Function Since the gradient of the tangent changes as we move along the graph, we can describe a gradient function for the graph. This is called the derived function or the derivative function of the curve. We represent the derivative function by 𝑑𝑦 𝑑𝑥 given y in terms of x. We represent the derivative function by f’(x) given the function f(x).

Example:

Rules of Differentiation Differentiation is the process of finding a derivative or gradient function. Rules for differentiating:

Example:

Equations of Tangents

Example:

Normals to Curves

Example: