Differentiation and Functional Notation

Front

What is functional notation?

Back

An equation written in the form of f(x) is called functional notation.

Front

How can you think of functions in terms of input and output?

Back

Think of functions like a machine where you input x and it produces f(x) as the output.

Front

What is the gradient of a function?

Back

The gradient of a function at a point is the slope of the tangent line to the curve at that point.

Front

What is the process of finding the gradient function called?

Back

Differentiation.

Front

What does d(y)/d(x) represent?

Back

It represents the derivative of y with respect to x.

Front

How do you find the exact gradient at a point on a curve?

Back

1. Find the gradient function d(y)/d(x). 2. Substitute the x-coordinate of the point into the gradient function.

Front

What is the gradient function used for?

Back

To find the gradient of a curve at any point.

Front

What is the gradient of the curve y = x^2 at the point A(2,4)?

Back

The gradient can be found by differentiating y = x^2 and substituting x = 2.

Front

What is the common notation for the derivative of y with respect to x?

Back

d(y)/d(x) is a common notation used to denote the derivative.

Front

What are some other notations used for derivatives?

Back

Other commonly used notations include dy/dx, f'(x), and Df.