Find the Function f(x)=-x

$f (x) = - x$

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 $- 1$ is constant with respect to $x$ , move $- 1$ out of the integral.

$- \int x d x$

Step 3

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

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

Step 4

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

$- \frac{1}{2} x^{2} + C$

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.

$F (x) = - \frac{1}{2} x^{2} + C$