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Math Help - Derivative and Tangent Line

  1. #1
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    Derivative and Tangent Line

    Find the Derivative of 3x^2-4x+5

    lim x->0 I got 3(x+Δx)^2-4(x+Δx)+5-(3x^2-4x+5)
    Δx
    lim x->0 = 3(x^2+2xΔx+Δx)-4x-4Δx+5-3x^2+4x-5
    Δx
    lim x->0 = 3x^2+6xΔx+3Δx^2-4x-4Δx+5-3x^2+4x-5
    Δx
    lim x->0 = 6xΔx+3Δx-4
    Δx
    lim x->0 = Δx(6x+3Δx-4)
    Δx
    lim x->0 = 6x=3(0)-4

    6x-4


    Find an Equation of the Tangent Line to the Graph Above at the given point (2,9)

    f(x) = 3x^2-4x+5
    f`(x) = 6x-4
    f`(x) = 6(2)-4 = 12-4 = 8
    y-8=8(x-2)
    y=8x-8


    Are these right? If not can anyone help me?
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  2. #2
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    Re: Derivative and Tangent Line

    Quote Originally Posted by Deo3560 View Post
    Find the Derivative of 3x^2-4x+5

    lim x->0 I got 3(x+Δx)^2-4(x+Δx)+5-(3x^2-4x+5)
    Δx
    lim x->0 = 3(x^2+2xΔx+Δx)-4x-4Δx+5-3x^2+4x-5
    Δx
    lim x->0 = 3x^2+6xΔx+3Δx^2-4x-4Δx+5-3x^2+4x-5
    Δx
    lim x->0 = 6xΔx+3Δx-4
    Δx
    lim x->0 = Δx(6x+3Δx-4)
    Δx
    lim x->0 = 6x=3(0)-4

    6x-4


    Find an Equation of the Tangent Line to the Graph Above at the given point (2,9)

    f(x) = 3x^2-4x+5
    f`(x) = 6x-4
    f`(x) = 6(2)-4 = 12-4 = 8
    y-8=8(x-2)
    y=8x-8


    Are these right? If not can anyone help me?
    f(x) = 3x^2-4x+5

    f'(x) = 6x-4

    f'(2) = 8

    tangent line equation at the point (2,9) ...

    y-9 = 8(x-2)
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  3. #3
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    Re: Derivative and Tangent Line

    thank you
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