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March 28, 2017

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Use the four step process to find the slope of the tangent line to the graph at any point:

f(x) = -1/2(x^2)

  • calculus please help - ,

    f(x) = -1/2(x^2)

    Step 1
    f(x + h)= -1/2(x + h)^2
    f(x + h)= -1/2(x^2 + 2xh + h^2)
    f(x + h)= -1/2 x^2 - xh - 1/2 h^2

    Step 2
    f(x + h)-f(x)= -1/2 x^2 - xh - 1/2 h^2 - (-1/2 x^2)

    f(x + h)-f(x)= -1/2 x^2 - xh - 1/2 h^2 + 1/2 x^2

    f(x + h) - f(x) = -xh - 1/2 h^2
    f(x + h) - f(x) = h (-x - 1/2 h)

    Step 3
    (f(x + h) - f(x))/h = (h(-x - 1/2 h))/h
    (f(x + h) - f(x))/h = -x - 1/2 h

    Step 4
    Evaluate lim h-->0
    lim h-->0 = -x - 1/2 (0)
    lim h-->0 = -x

    Dx(-1/2 x^2) = -x

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