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What is the instantaneous rate of change of #f(x)=x/(-x+7 )# at #x=0 #?

Answer 1

Cameron Alexander

The instantaneous rate of change is the first derivative calculated at #x=0#

Hence

#f'(x)=7/(7-x)^2#

so #f'(0)=7/7^2=1/7#

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Answer 2

Christopher Agresta

To find the instantaneous rate of change of ( f(x) = \frac{x}{-x + 7} ) at ( x = 0 ), you can use the concept of the derivative.

Find the derivative of the function ( f(x) ) with respect to ( x ).
Evaluate the derivative at ( x = 0 ) to find the instantaneous rate of change.

The derivative of ( f(x) ) with respect to ( x ) can be found using the quotient rule or by simplifying the function first and then differentiating. After finding the derivative, substitute ( x = 0 ) to find the instantaneous rate of change at that point.

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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.