How do you estimate the instantaneous rate of change for #f(x) = 3/x# at #x=2#?
-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.
From here, we can obtain the derivative function by applying the power rule of derivatives.
We can now enter our given, x=2, and obtain the solution.
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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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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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