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

Mar 29, 2018

$3$

#### Explanation:

"Instantaneous rate of change of $f \left(x\right)$ at $x = a$" means "derivative of $f \left(x\right)$ 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 $f ' \left(a\right) .$

$f \left(x\right) = 3 x + 5$

$f ' \left(x\right) = 3$, 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 $3$.

Mar 29, 2018

$3$

#### 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.

$f \left(x\right) = 3$

so at $f \left(1\right) = 3$ so that is the instantaneous rate of change.