Gr12 Mathematics: Ch 5.7 Application of Differential Calculus

What is the primary application of differential calculus in graph sketching?

Determining the stationary points of a function (correct)

Calculating the area under a curve

Finding the maximum or minimum of a function

Solving equations of motion

What is the derivative used to find in a function?

The minimum value of a function

The maximum value of a function

The instantaneous rate of change (correct)

The average rate of change over an interval

In optimisation problems, what is being maximised or minimised?

A rate of change

A variable (correct)

A function's graph

A stationary point

What is the term used to describe how one quantity changes in relation to another?

Rate of change Signup and view all the answers

What is calculated over an interval in differential calculus?

Average rate of change Signup and view all the answers

What is the advantage of determining the stationary points of a function?

To sketch the graph of the function more accurately Signup and view all the answers

What is the relationship between the instantaneous rate of change and the average rate of change?

The average rate of change is calculated over an interval, while the instantaneous rate of change is calculated at a point Signup and view all the answers

Which of the following is an example of an optimisation problem?

Finding the maximum value of a function Signup and view all the answers

What does the derivative of a function represent?

The slope of the tangent line to the function Signup and view all the answers

What is the importance of determining the rate of change in real-world applications?

It allows us to model and analyse real-world phenomena Signup and view all the answers

Gr12 Mathematics: Ch 5.7 Application of Differential Calculus

Questions and Answers

What is the primary application of differential calculus in graph sketching?

What is the derivative used to find in a function?

In optimisation problems, what is being maximised or minimised?

What is the term used to describe how one quantity changes in relation to another?

What is calculated over an interval in differential calculus?

What is the advantage of determining the stationary points of a function?

What is the relationship between the instantaneous rate of change and the average rate of change?

Which of the following is an example of an optimisation problem?

What does the derivative of a function represent?

What is the importance of determining the rate of change in real-world applications?

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