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Math Help - Evaluate difference quotient

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    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}
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    Quote Originally Posted by windir View Post
    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.
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    Quote Originally Posted by windir View Post
    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
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    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!
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