How do you estimate the instantaneous rate of change for #f(x) = 3/x# at #x=2#?

Answer 1

-3/4 is the instantaneous rate of change at x=2.

The equation in this particular problem can be rewritten as follows: The derivative of the equation can be found to determine the instantaneous rate of change.

#f(x) = 3(x^-1)#

From here, we can obtain the derivative function by applying the power rule of derivatives.

#f'(x) = -3(x^-2)# or #f'(x) = -3/x^2#

We can now enter our given, x=2, and obtain the solution.

#f'(2) = -3/4#
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Answer 2

To estimate the instantaneous rate of change for ( f(x) = \frac{3}{x} ) at ( x = 2 ), you can use the formula for the derivative of ( f(x) ), which is ( f'(x) ). The derivative of ( f(x) = \frac{3}{x} ) is ( f'(x) = -\frac{3}{x^2} ). Plugging in ( x = 2 ) into this derivative formula gives ( f'(2) = -\frac{3}{2^2} = -\frac{3}{4} ). Therefore, the instantaneous rate of change of ( f(x) = \frac{3}{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.

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.

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.

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.

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