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

Answer 1

Ezekiel Alexander

#-#2 ( 1 + e ), e = 2.718281828....

#d/dx#f(x) = #-#e^x #-#xe^x #-#2x

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Answer 2

Christopher Allers

To find the slope of the function (f(x) = -xe^x - x^2) at (x = 1), we need to take the derivative of (f(x)) with respect to (x), and then evaluate it at (x = 1). The derivative of (f(x)) is (f'(x) = -e^x - xe^x - 2x). Evaluating (f'(x)) at (x = 1) gives (f'(1) = -e^1 - 1e^1 - 2(1) = -e - e - 2 = -2e - 2). Therefore, the slope of (f(x)) at (x = 1) is (-2e - 2).

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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.