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opus
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These are the two things that I'm going over in my PreCalculus class- the Difference Quotient and the Average Rate of Change of a Function. I'm confused as to what exactly they are, and how they relate to each other.
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.
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.