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What is the slope of #f(x)=-e^x+3# at #x=-1#?

Answer 1

Charles Arocha

#- 1/e#

#f(x)=-e^x+3#

#f'(x)=-e^x#

#f'(-1)=-e^(-1) = - 1/e#

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Answer 2

Charles Arocha

To find the slope of the function ( f(x) = -e^x + 3 ) at ( x = -1 ), we need to find the derivative of the function and then evaluate it at ( x = -1 ).

The derivative of ( f(x) = -e^x + 3 ) is ( f'(x) = -e^x ).

Evaluating the derivative at ( x = -1 ), we get:

( f'(-1) = -e^{-1} = -\frac{1}{e} )

Therefore, the slope of ( f(x) = -e^x + 3 ) at ( x = -1 ) is ( -\frac{1}{e} ).

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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.