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calculus anti-derivation

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Given that the graph of f(x) passes through the point (2,5) and that the slope of its tangent line at (x, f(x))is 3x+5, what is f(3) ?

  • calculus anti-derivation - ,

    if dy/dx = 3x+5 , then
    y = (3/2)x^2 + 5x + c

    when x=2, y = 5
    5 = (3/2)(4) + 10 + c
    5 = 6 + 10 + c
    c = -11

    f(x) = (3/2)x^2 + 5x - 11
    f(3) = (3/2)(9) +15 - 11 = 35/2

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