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Math Help - Evaluate the difference quotient for the function f(x) = 2 - 2x - X^2

  1. #1
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    Evaluate the difference quotient for the function f(x) = 2 - 2x - X^2

    Consider the function: f(x) = 2 - 2x - X^2

    Evaluate the difference quotient for the given function. Simplify your answer.
    f(2+h) - f(2) / h

    I found f(2+h) = (-6 -6h -h^2)
    I found f(2) = (-22)

    Can this be simplified any more?
    Please show me how.
    -h^2 -6h +16 / h
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  2. #2
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    I don't know why you've evaluated the function at x = 2...

    It should be

    \frac{f(x + h) - f(x)}{h}...
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  3. #3
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    Quote Originally Posted by superduper1 View Post
    Consider the function: f(x) = 2 - 2x - X^2

    Evaluate the difference quotient for the given function. Simplify your answer.
    f(2+h) - f(2) / h

    I found f(2+h) = (-6 -6h -h^2)
    I found f(2) = (-22)

    Can this be simplified any more?
    Please show me how.
    -h^2 -6h +16 / h
    f(2+h) = 2 - 2(2+h) - (2+h)^2

    f(2+h) = 2 - 4 - 2h - (4 + 4h + h^2)

    f(2+h) = -6 - 6h - h^2

    f(2) = 2 - 2(2) - 2^2 = -6

    try again
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