What is the relation between limits, derivatives and

oerddrwsmqc

oerddrwsmqc

Answered question

2022-03-15

What is the relation between limits, derivatives and instantaneous rate of change?

Answer & Explanation

Jamiya Bradford

Jamiya Bradford

Beginner2022-03-16Added 6 answers

Depending on how we are interpreting the difference quotient we get either a derivative, the slope of a tangent line or an instantaneous rate of change.
A derivative is defined to be a limit. It is the limit as h\rightarrow 0 of the difference quotient
f(x+h)f(x)h
The instantaneous rate of change is also a limit. It is a limit of an average rate of change. Because the average rate of change is expressed as f(x+h)f(x)h, the instantaneous rate of change is also a limit of the difference quotient.

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