Evaluate difference quotient

**windir** · January 24th 2010, 10:16 PM

This is actually from my calculus textbook, but its in the first chapter which is all pre-calculus review. Unfortunately, I never was taught about difference quotients. Do they come up in calculus alot? Anyway, here's the prob:
If $f(x)=x^2-2x+3$ , evaluate the difference quotient
$\frac{f(a+h)-f(a)}{h}$

**Jhevon** · January 24th 2010, 11:17 PM

Originally Posted by windir

This is actually from my calculus textbook, but its in the first chapter which is all pre-calculus review. Unfortunately, I never was taught about difference quotients. Do they come up in calculus alot? Anyway, here's the prob:
If $f(x)=x^2-2x+3$ , evaluate the difference quotient
$\frac{f(a+h)-f(a)}{h}$

yes, this shows up in calculus a lot. it is used to define the derivative, a very important concept in calculus.

anyway, $f(a + h) = (a + h)^2 - 2(a + h) + 3$ and $f(a) = a^2 - 2a + 3$ . Plug these into the difference quotient, expand the brackets and simplify. your main objective is to cancel the $h$ in the denominator.

**tonio** · January 24th 2010, 11:19 PM

Originally Posted by windir

This is actually from my calculus textbook, but its in the first chapter which is all pre-calculus review. Unfortunately, I never was taught about difference quotients. Do they come up in calculus alot? Anyway, here's the prob:
If $f(x)=x^2-2x+3$ , evaluate the difference quotient
$\frac{f(a+h)-f(a)}{h}$