Find the antiderivative $F$ of $f$ defined by $f (x) = 4 x^{3} - 6$ , where $f (0) = 3$

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Solution

$\begin{matrix} f (x) = 4 x^{3} - 6 \int 4 x^{3} - 6 d x f (x) = \frac{4 x^{4}}{4} - 6 x + C f (0) = 3 {(0)}^{4} - 6 (0) + C = 3 f (x) = x^{4} - 6 x + 3 \end{matrix}$

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