- #1

opus

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**Average Rate of Change**= ##\frac {f \left(b\right) - f\left(a\right)} {b - a }##

To my understanding, this is the average rate of change of the function from value b to value a. Getting something like a value of 10 for this would make sense. However, in some of the examples such as:

Find the average rate of change of ##f\left(x\right)=2x^2-3## as x changes from x=c to x=c+h and h cannot equal 0.

##\frac {f \left(c+h\right) - f\left(c\right)} {\left(c+h\right) - c }##,

and yields the result

=4c+2h

What does this even mean?

As for the difference quotient,

**Difference Quotient**= ##\frac {f \left(x+h\right) - f\left(x\right)} {h}##, h cannot equal 0.

Is this equation stating the difference from the value of the function f at x+h to the value of the function f at x? What is the purpose of the h?

I don't have a problem computing these, I just don't know what they're saying or what the purpose is behind them.