# How do you find the instantaneous rate of change of #f(x)=x^2-2/x+4# at #x=-1#?

##### 1 Answer

At

#### Explanation:

When you calculate a function's derivative, you obtain an other function representing the variations of the first function's curve's slope.

A curve's slope is the instantaneous variation rate of the curve's function at a given point.

Therefore, if you are looking for the instantaneous variation rate of a function at a given point, you should calculate this function's derivative at said point.

In your case:

Calculating the derivative:

Now, you just need to replace

The derivative is null, therefore the instantaneous change rate is null and the function doesn't increase or decrease at this specific point.