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How do you find the instantaneous rate of change of the function #F(x) = e^x# when x=0?

Answer 1

Emma Aldridge

The instantaneous rate of change at #x=0# equals with numerical value of the first derivative at #x=0#

Hence #[(d(f(x)))/dx]_(x=0)=[e^x]_(x=0)=e^0=1#

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Answer 2

Christopher Agresta

To find the instantaneous rate of change of the function ( F(x) = e^x ) when ( x = 0 ), you can calculate the derivative of ( F(x) ) with respect to ( x ) and then evaluate it at ( x = 0 ). The derivative of ( e^x ) is itself, so ( F'(x) = e^x ). Evaluating this derivative at ( x = 0 ) gives the instantaneous rate of change at that point, which is ( F'(0) = e^0 = 1 ). Therefore, the instantaneous rate of change of ( F(x) = e^x ) when ( x = 0 ) is 1.

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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.