Evaluate difference quotient

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Jan 24th 2010, 10:16 PM
windir

Evaluate difference quotient

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
$\frac{f(a+h)-f(a)}{h}$
Jan 24th 2010, 11:17 PM
Jhevon

Quote:

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.
Jan 24th 2010, 11:19 PM
tonio

Quote:

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
$\frac{f(a+h)-f(a)}{h}$

$\frac{f(a+h)-f(a)}{h}=\frac{(a+h)^2-2(a+h)+3-(a^2-2a+3)}{h}$ . Now just open parentheses and make some order there.

Tonio
Jan 24th 2010, 11:41 PM
windir

awesome! so working from there i got:
$\frac{a^2+2ah+h^2-2a-2h+3-(a^2-2a+3)}{h}$
$\frac{2ah+h^2-2h}{h}$
$2a+h-2$
which is right! thanks guys!