Find the Function f(x)=4x^3

$f (x) = 4 x^{3}$

Step 1

The function $F (x)$ can be found by evaluating the indefinite integral of the derivative $f (x)$ .

$F (x) = \int f (x) d x$

Step 2

Since $4$ is constant with respect to $x$ , move $4$ out of the integral.

$4 \int x^{3} d x$

Step 3

By the Power Rule, the integral of $x^{3}$ with respect to $x$ is $\frac{1}{4} x^{4}$ .

$4 (\frac{1}{4} x^{4} + C)$

Step 4

Simplify the answer.

Rewrite $4 (\frac{1}{4} x^{4} + C)$ as $4 (\frac{1}{4}) x^{4} + C$ .

$4 (\frac{1}{4}) x^{4} + C$

Simplify.

Combine $4$ and $\frac{1}{4}$ .

$\frac{4}{4} x^{4} + C$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{4} x^{4} + C$

Rewrite the expression.

$1 x^{4} + C$

Multiply $x^{4}$ by $1$ .

$x^{4} + C$

Step 5

The function $F$ if derived from the integral of the derivative of the function. This is valid by the fundamental theorem of calculus.

$F (x) = x^{4} + C$