How do you find the instantaneous rate of change of the function f(x) = 3/x when x=2?

1 Answer
Ken C.
Mar 25, 2016

Take the derivative of f(x) and evaluate it at x=2 to get -3/4.

Explanation:

Instantaneous rate of change is simply the derivative of a function at a point. So begin by finding the derivative of f(x) using the power rule:
f(x)=3/x=3x^(-1)
f'(x)=-1*3^(-1-1)=-3x^(-2)

Now we evaluate it at x=2 to find instantaneous rate of change:
f'(x)=-3x^(-2)
f'(2)=-3(2)^(-2)=-3(1/4)=-3/4

Therefore the instantaneous rate of change of f(x)=3/x at x=2 is -3/4.

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