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Math Help - A few quick questions!

  1. #1
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    A few quick questions!

    Hey! A few questions here:

    1) Find the equation of the tangent line to the parabola y=6-5x+3x^2 at the point where x=1. I got y=x+3... but the book says y=x+2.

    2) Fine the equation of both tangent lines to the curve y=x^3-x that are parallel to the line 22x-2y+1=0. I understand y=11x+16.. but not the second answer.. y=11x-16.

    3) What's the derivative of 5^x-1?

    ANY HELP IS VERY, VERY, VERY MUCH APPRECIATED! Thanks.
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  2. #2
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    Quote Originally Posted by Sculthorp View Post
    Hey! A few questions here:

    1) Find the equation of the tangent line to the parabola y=6-5x+3x^2 at the point where x=1. I got y=x+3... but the book says y=x+2.

    y(1) = 4
    y' = -5 + 6x
    y'(1) = 1

    y - 4 = 1(x - 1)
    y = x + 3

    correct


    2) Fine the equation of both tangent lines to the curve y=x^3-x that are parallel to the line 22x-2y+1=0. I understand y=11x+16.. but not the second answer.. y=11x-16.

    22x - 2y + 1 = 0 has slope, m = 11

    y' = 3x^2 - 1 = 11

    x = 2 ... y = 6

    y - 6 = 11(x - 2)

    y = 11x - 16

    x = -2 ... y = -6

    y + 6 = 11(x + 2)


    y = 11x + 16


    3) What's the derivative of 5^x-1?

    5^x - 1 or 5^{x-1} ?
    ok?
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  3. #3
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    Thanks so much! I meant 5^{x-1} though!
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  4. #4
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    if u is a function of x and a is a positive constant ...

    \frac{d}{dx} [a^u] = a^u \cdot \frac{du}{dx} \cdot \ln{a}
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