Seeing a function and its derivative together
Turn on the derivative and look at where the dashed amber curve crosses zero: exactly where f1 has a horizontal tangent (a peak, valley or flat inflection). Where f1 climbs, f1′ is positive; where it falls, negative. Then switch on the integral: its slope at every point is the height of f1, which is the Fundamental Theorem of Calculus drawn as a picture.
For a single function with a full step-by-step derivative, use the derivative calculator. For shaded areas, use the area under the curve calculator.
Questions students ask
What can this grapher show that a normal graphing calculator can’t?
It draws the derivative f′ and an accumulated integral ∫0xf(t)dt alongside your function, so you can see how the three are related: where f′ crosses zero, f has a peak or valley; where f crosses zero, the integral curve peaks or bottoms out.
How many functions can I plot?
Up to four at once, each in its own colour, plus the derivative and integral of the first one.
How do I zoom?
Set the x-range with the two boxes, or use the zoom buttons. The y-range fits automatically to the visible curves.
Is my graph saved?
Your functions are kept in the page address, so bookmark or share the link to come back to the same graph.