Question

What is the instantaneous rate of change of `f(x)=3x+5` at `x=1`?

Answer 1

`3`

Explanation:

"Instantaneous rate of change of `f(x)` at `x=a`" means "derivative of `f(x)` at `x=a`.

The derivative at a point represents the function's rate of change at that point, or the instantaneous rate of change, often represented by a tangent line with the slope `f'(a).`

`f(x)=3x+5`

`f'(x)=3`, the derivative of a constant is zero, meaning the five plays no role here.

So, at `x=1,` or at any `x` actually, the rate of change is `3`.

Answer 2

`3`

Explanation:

Rate of change is just the gradient function and the instantaneous rate of change is just the gradient function at a particular point

So to get the gradient function you merely have to differentiate the original function.

`f(x)=3`

so at `f(1)=3` so that is the instantaneous rate of change.