AROC → IROC Explorer
Use nearby average rates of change to estimate an instantaneous rate of change.
Secant line AB — slope = AROCTangent line at A — slope = IROCΔt and Δs
Live values
Functions(t) = t²
Fixed point A(2, 4)
Movable point B(3.00, 9.00)
Δt = b − 21.00
Δs = s(b) − 45.00
AROC = Δs / Δt
5.000
5.00 / 1.00
B is exactly on A, soΔt = 0 and the quotient is 0/0 —undefined. There is no secant line through a single point. The tangent line is still there, and IROC is still4: the limit describes where the AROC values are heading, not the value at b= 2.
IROC at A
4
slope of the tangent line
Drag point B
Jump to:
- Average Rate of Change (AROC)
- Change over an interval.
- Instantaneous Rate of Change (IROC)
- Change at one instant.
Key idea
- AROC = slope of a secant line= rise / run
- IROC = slope of the tangent line at the point
- Nearby AROCs can estimate IROC
A limit asks where the function is going, not where it is.