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

Answer 1

Ezekiel Alexander

Slope of #f(x)# at #x = 1# is #0#

#f(x) = -x * e^x/x^2# #= -e^x/x# = #-e^x*x^-1#

#f'(x) = -(e^x*(-x^-2) + x^-1*e^x )# (Product, Exponential and Power Rules)

The slope of #f(x)# at #x=1# is given by #f'(1)#

#f'(1) = -(e^1 * (-1) + e^1 *1)#

#f'(1) = -(-e+e) = 0#

Hence: Slope of #f(x)# at #x = 1# is #0#

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Answer 2

Christopher Agresta

To find the slope of the function ( f(x) = -\frac{xe^x}{x^2} ) at ( x = 1 ), you can use the formula for finding the derivative of a function. Then, evaluate the derivative at ( x = 1 ) to find the slope 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.