The Derivative Graph Calculator helps you visualize the derivative of a function and connect the slope of the original curve with its graph.
What a derivative graph shows
If the original function is f(x), its derivative is f'(x). At each x-value, f'(x) gives the instantaneous slope of f(x). Positive values mean the original function is increasing, negative values mean it is decreasing, and a zero derivative indicates a horizontal tangent.
Worked example
For f(x) = xΒ², the derivative is f'(x) = 2x. At x = 3, the slope is 6. At x = 0, the slope is 0, which agrees with the flat tangent at the vertex.
How to read the graph
- Enter the function supported by the calculator.
- Generate the derivative and its graph.
- Look for zeros of f'(x), where the original curve may have a stationary point.
- Check sign changes to distinguish increasing and decreasing intervals.
Why it is useful
Viewing the derivative makes rate of change easier to understand and provides a visual way to check turning points, slopes, and intervals of increase or decrease.