Investigate how the derivative of a curve relates to the curve in terms of x values and slope of tangent to curve.

Move the point on the curve around to show how the tangent to the curve changes Click on checkboxes 'x values' to show relationship between x value of point on curve, and x value of derived function Click on checkbox 'Slope of f(x)' to show relationship between slope of tangent and y value of derived function. Click on checkbox 'Derived Function to show trace of derived function as x value of original function changes.

Investigate the relationships between the function f(x) and its first and second derivatives in terms of the slopes of its tangent and the y value of f'(x), and similarly the slope of f'(x) and y value of f''(x)

Click checkboxes to show the function f(x) and its first and second derivative. Move the point on the f(x) and investigate relationship between the tangent and 1st derivative. Move point on f'(x) and investigate relationship between 1st and second derivative. Move slider to change gradient of f(x) and see how it affects 1st derivative and second derivative.