Question

If f(x) = 5x+27, find the instantaneous rate of change of f(x) at x=9

Answer 1

The instantaneous rate of change refers to the derivative of f(x), so let's find that first, following the power rule, we have.

$f^{\prime}(x)=1\cdot5x^{1-1}=5x^0=5\cdot1=5$

As you can observe, the instantaneous rate of change is a constant, which means we don't have to evaluate it at x=9.

Therefore, the instantaneous rate of change is f'(x) = 5.