If f'(x) = 4x^5 - 6x and f(0) = 3 , then f(3) is equal to

The correct answer is Option (1) → 462

f is an antiderivative of f′:

    \( \displaystyle f(x) = \int (4x^5 - 6x)\,dx \)

    \( \displaystyle = \frac{4x^6}{6} - \frac{6x^2}{2} + C \)

    \( \displaystyle = \frac{2}{3}x^6 - 3x^2 + C \)

The condition f(0) = 3 fixes the constant:

    \(C = 3\)

So

    \( \displaystyle f(3) = \frac{2}{3}(729) - 3(9) + 3 \)

    \(= 486 - 27 + 3 = 462\)