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

Answer 1

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

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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Answer 2

Christopher Agresta

To find the instantaneous rate of change of the function ( f(x) = \frac{3}{x} ) when ( x = 2 ), you can use the derivative of the function. The derivative of ( f(x) ) with respect to ( x ) is given by ( f'(x) = \frac{-3}{x^2} ). Evaluating this derivative at ( x = 2 ), you get ( f'(2) = \frac{-3}{2^2} = -\frac{3}{4} ). So, the instantaneous rate of change of ( f(x) ) at ( 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.