How this calculation works
Find the point where the tangent slope equals the interval’s secant slope.
THE FORMULA
For a nonconstant derivative of a quadratic, c=(left+right)/2A worked example
On [2,6], the point is x=4.
Good to know
A linear function has the same slope throughout the interval.
Reference: OpenStax Calculus Volume 3 (opens in a new tab) ↗
Read the result
Find the point where the tangent slope equals the interval’s secant slope.
The primary result is labeled “Mean value theorem x”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
A linear function has the same slope throughout the interval.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
On [2,6], the point is x=4.
Which rule does this calculator apply?
For a nonconstant derivative of a quadratic, c=(left+right)/2