Rates of Change

Identifying Increasing/Decreasing or Constant sections of Function Domains

Linear Rates of Change

Average Rates of Change

Gradients of tangents

Average Vs Instantaneous Rates of Change

Gradient of a Curve (NSW Specific)

Equations of Tangent Lines

Difference Quotients

Limit and First Principle (investigation) LIVE

The Derivative as a Limit - Limiting Chord Process

Practical Applications of Rates of Change

Relating gradient and original functions (investigation) - including velocity time to position time

Class XI

Gradients of tangents

Interactive practice questions

Consider the function $f\left(x\right)=1$f(x)=1 shown here.

If we were to draw a tangent to the function for any $x$x value, what is the gradient of that tangent?

Loading Graph...

Easy

< 1min

Consider the function $f\left(x\right)=2x-4$f(x)=2x−4 shown here.

If we were to draw a tangent to the function for any $x$x value, what is the gradient of that tangent?

Easy

< 1min

What is the gradient of the tangent at the given point?

Easy

< 1min

What is the gradient of the tangent at the given point?

Easy

< 1min

Outcomes

11.C.LD.1

Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

What is Mathspace

About Mathspace