Sketching Gradient Functions
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
