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Math Help - Secant Line Slope Formula

  1. #1
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    Secant Line Slope Formula

    Im stuck on this problem and don't know what to do.

    Using the formula for the slope of a secant line passing through two points on a curve f(x+h)-f(x)/h determine this secant line slope formula for the function f(x)=3x^2-5x. Yu must simplify your result algebraically.
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  2. #2
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    Quote Originally Posted by oregon88 View Post
    Im stuck on this problem and don't know what to do.

    Using the formula for the slope of a secant line passing through two points on a curve f(x+h)-f(x)/h determine this secant line slope formula for the function f(x)=3x^2-5x. Yu must simplify your result algebraically.
    Just plug it in?

    For example, if f(x) = 93x, and if you want f(x+h), you will write f(x+h) = 93(x+h).
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  3. #3
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    So I would do (3x^2-5x)(x+h)-(3x^2-5x)(x)/h?
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  4. #4
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    Quote Originally Posted by oregon88 View Post
    So I would do (3x^2-5x)(x+h)-(3x^2-5x)(x)/h?
    Hmm, not so much, look at this

    g(x) = 2x^2

    g(5) = 2(5)^2

    g(x+a) = 2(x+a)^2

    you replace every "x" on the right hand side with whatever's in parentheses after the g on the left hand side.. make sense?

    Edit: changed from letter f to letter g to avoid potential confusion.
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  5. #5
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    so then it would be f((3x^2-5x)+h)-f(3x^2-5x)/h?
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  6. #6
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    Quote Originally Posted by oregon88 View Post
    so then it would be f((3x^2-5x)+h)-f(3x^2-5x)/h?
    Ok, write

    f(x) = 3x^2-5x

    f(x+h) = ?

    Now think of x+h as a single number (because that's what it is). So you understand that

    f(7) = 3(7)^2-5(7) right?

    Now using the same method, try to replace the question mark below with the appropriate expression

    f(x+h) = ?
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  7. #7
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    Ok, write

    f(x) = 3x^2-5x

    f(x+h) = ?

    Now think of x+h as a single number (because that's what it is). So you understand that

    f(7) = 3(7)^2-5(7) right?

    Now using the same method, try to replace the question mark below with the appropriate expression

    f(x+h) = 3(x+h)^2 - 5(x+h)

    So whould I continue and do f(x+h) - f(x)/h and get 6x + 3h -5 in the end?
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  8. #8
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    Quote Originally Posted by oregon88 View Post
    f(x+h) = 3(x+h)^2 - 5(x+h)
    This is good.

    Quote Originally Posted by oregon88 View Post
    So whould I continue and do f(x+h) - f(x)/h and get 6x + 3h -5 in the end?
    Yes, I also get this. Good job!

    By the way, it really is better practice to write parentheses, like this:

    (f(x+h) - f(x))/h

    This way respects the standard order of operations.
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  9. #9
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    Difference quotient

    The big butt-kicker about diff quotient problems is sign errors, so be on your toes! My solution is attached. Sorry, not too great at latex yet.

    Be Well,
    T
    Attached Files Attached Files
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