Find the Function f(x)=3x

$f (x) = 3 x$

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 $3$ is constant with respect to $x$ , move $3$ out of the integral.

$3 \int x d x$

Step 3

By the Power Rule, the integral of $x$ with respect to $x$ is $\frac{1}{2} x^{2}$ .

$3 (\frac{1}{2} x^{2} + C)$

Step 4

Simplify the answer.

Rewrite $3 (\frac{1}{2} x^{2} + C)$ as $3 (\frac{1}{2}) x^{2} + C$ .

$3 (\frac{1}{2}) x^{2} + C$

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2} x^{2} + C$

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.

$F (x) = \frac{3}{2} x^{2} + C$