Illustration of Second Derivitive

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.