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What is the slope of #f(x)=-e^x+2x# at #x=1#?

Answer 1

Ezra Adams

#2-e#

Find #f'(1)#.

To find #f'(x)#, the most important thing to know is that the derivative of #e^x# is still #e^x#.

Since the derivative of #2x# is just #2#,

#f'(x)=-e^x+2#

To find the slope (of the tangent line) at that point, plug in #1#.

#f(1)=-e^1+2=2-eapprox-0.7183#

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Answer 2

Scarlett Allison

To find the slope of the function ( f(x) = -e^x + 2x ) at ( x = 1 ), we first need to find the derivative of the function, ( f'(x) ), and then evaluate it at ( x = 1 ).

The derivative of ( f(x) ) is ( f'(x) = -e^x + 2 ).

Now, to find the slope at ( x = 1 ), we substitute ( x = 1 ) into ( f'(x) ): [ f'(1) = -e^1 + 2 = -e + 2 ]

So, the slope of the function ( f(x) ) at ( x = 1 ) is ( -e + 2 ) or approximately ( -0.7183 ).

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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.