# Slope of a Curve at a Point

## Key Questions

• The slope of a curve of $y = f \left(x\right)$ at $x = a$ is $f ' \left(a\right)$.

Let us find the slope of $f \left(x\right) = {x}^{3} - x + 2$ at $x = 1$.

By taking the derivative,
$f ' \left(x\right) = 3 {x}^{2} - 1$

By plugging in $x = 1$,
$f ' \left(1\right) = 3 {\left(1\right)}^{2} - 1 = 2$

Hence, the slope is $2$.

• First you need to find $f ' \left(x\right)$, which is the derivative of $f \left(x\right)$.

$f ' \left(x\right) = 2 x - 0 = 2 x$

Second, substitute in the value of x, in this case $x = 1$.

$f ' \left(1\right) = 2 \left(1\right) = 2$

The slope of the curve $y = {x}^{2} - 3$ at the $x$ value of $1$ is $2$.