# How do I find the instantaneous velocity of a curve?

##### 1 Answer
Sep 28, 2014

The instantaneous velocity is found by taking the derivative of the curve and then substituting in a value of x.

Example:

$f \left(x\right) = {x}^{3}$

$f ' \left(x\right) = 3 {x}^{2}$

Below are the instantaneous velocities at various values of $x$ for the curve.

$x = - 3 \to f ' \left(- 3\right) = 3 {\left(- 3\right)}^{2} = 27$

$x = 0 \to f ' \left(0\right) = 3 {\left(0\right)}^{2} = 0$

$x = 1 \to f ' \left(1\right) = 3 {\left(1\right)}^{2} = 3$

$x = 5 \to f ' \left(5\right) = 3 {\left(5\right)}^{2} = 75$