math calculus

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Find the equation of the function f whose graph passes through the point (0, 4/3) and whose derivative is

f'(x) = x sqrt 16 − x^2
.

f(x) =

  • math calculus -

    Did you mean

    f'(x) = x√(16-x^2) ??? , brackets are needed here.

    then f(x) = (-1/3)(16 - x^2)^(3/2) + c
    (differentiate to confirm)

    if x = 4/3 , f(4/3) = 0

    0 = (-1/3)(16 - 16/9)^(3/2) + c

    solve for c and sub back into f(x) =

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