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Math Help - derivative problem

  1. #1
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    derivative problem

    1) The derivative of f( x) at x = a can best be described graphically as:
    A) Average value of the function, f( x), between x = 0 and x = a.
    B) The slope of the line perpendicular to the graph of f (x) and containing the point (a,f(a)).
    C) The slope of the line containing the two points (0, f(0) ) and (a, f (a)).
    D) The slope of the tangent line to the graph of f (x) at the point (a, f(a) ).

    I picked D for this one.

    2) If f(x)= 8(sqrt x) + 6x^(3/4), find f '(x).

    A) 4x^(1/2) + (9/2)x^1/4

    B) 4x^(-1/2) + 8x^-1/4

    C) 4(sqrt x) + (18/4)x^1/2

    D) 4x^(-1/2) + (9/2)x^-1/4

    Im really confused about this one. I would guess A, but not sure.
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  2. #2
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    Re: derivative problem

    D is correct for (1)

    For (2), the rule for differentiating x raised to some power is ' power down to the front, subtract 1 from the power '.

    \sqrt{x} = x^{1/2}, so ... ?
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  3. #3
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    Re: derivative problem

    Im thinking A?
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  4. #4
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    Re: derivative problem

    No, D
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  5. #5
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    Re: derivative problem

    Quote Originally Posted by salma View Post
    No, D
    Yup!

    -Dan
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