Difference Quotient Calculator (Free)
Use this free difference quotient calculator to compute [f(x + h) − f(x)]/h — the average rate of change over a step of size h — and see how it approaches the derivative as h → 0, with a graph.
Why it matters
The difference quotient is the slope of the secant line over a step h. As h shrinks toward 0, it becomes the derivative — the foundation of differential calculus.
Original price was: $109.99.$54.99Current price is: $54.99.
How to use it
- Enter f(x), the point x, and the step h.
- Press Compute.
Related: the Derivative Calculator and the Average Rate of Change Calculator.
Frequently asked questions
What is the difference quotient?
[f(x + h) − f(x)] / h, the average slope of f over a step of size h.
Original price was: $109.99.$54.99Current price is: $54.99.
How does it relate to the derivative?
As h → 0, the difference quotient approaches f′(x), the instantaneous rate of change.
Original price was: $109.99.$54.99Current price is: $54.99.
Why can’t h be 0?
It would divide by zero; use a small nonzero h and watch the trend.
Original price was: $27.99.$17.99Current price is: $17.99.
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