How can I sketch a function's gradient function?
- Using your knowledge of gradients and derivatives you can use the graph of a function to sketch the corresponding gradient function
- The behaviour of a function tells you about the behaviour of its gradient function
Exam Tip
If f(x) is a smooth curve then f'(x) will also be a smooth curve.Take what you know about f'(x) (based on the table above) and then 'fill in the blanks' in between.If all you have is the graph of f(x) you will not be able to specify the coordinates of the y-intercept or any stationary points of f'(x).Be careful – points where f(x) cuts the x-axis don't tell you anything about the graph of f'(x)!
Worked Example
