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How to find instantaneous rate of change for #f(x) = 3/x# when x=2?

Answer 1

Ezra Adams

The instantaneous rate of change of #f(x)# is equal to the derivative of

#f(x)# at #x=2#

Hence

#(df(x)/dx)_(x=2)=(-3/x^2)_(x=2)=-3/2^2=-3/4#

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Answer 2

Ezekiel Alexander

To find the instantaneous rate of change of ( f(x) = \frac{3}{x} ) when ( x = 2 ), you can use the derivative of the function. The instantaneous rate of change at a specific point is given by the derivative of the function evaluated at that point. The derivative of ( f(x) = \frac{3}{x} ) is ( f'(x) = -\frac{3}{x^2} ). So, when ( x = 2 ), the instantaneous rate of change is ( f'(2) = -\frac{3}{2^2} = -\frac{3}{4} ). Therefore, the instantaneous rate of change of ( f(x) = \frac{3}{x} ) when ( x = 2 ) is ( -\frac{3}{4} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.