# Evaluate difference quotient

• 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 $\displaystyle f(x)=x^2-2x+3$, evaluate the difference quotient
$\displaystyle \frac{f(a+h)-f(a)}{h}$
• 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 $\displaystyle f(x)=x^2-2x+3$, evaluate the difference quotient
$\displaystyle \frac{f(a+h)-f(a)}{h}$

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

anyway, $\displaystyle f(a + h) = (a + h)^2 - 2(a + h) + 3$ and $\displaystyle f(a) = a^2 - 2a + 3$. Plug these into the difference quotient, expand the brackets and simplify. your main objective is to cancel the $\displaystyle h$ 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 $\displaystyle f(x)=x^2-2x+3$, evaluate the difference quotient
$\displaystyle \frac{f(a+h)-f(a)}{h}$

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

Tonio
• Jan 24th 2010, 11:41 PM
windir
awesome! so working from there i got:
$\displaystyle \frac{a^2+2ah+h^2-2a-2h+3-(a^2-2a+3)}{h}$
$\displaystyle \frac{2ah+h^2-2h}{h}$
$\displaystyle 2a+h-2$
which is right! thanks guys!