Is #f(x)=1/x-1/x^3+1/x^5# increasing or decreasing at #x=-1#?

Answer 1

Decreasing.

Rewrite

#f(x) = x^-1 - x^-3 + x^-5#

Distinguish:

#f'(x) = -x^-2 - (-3x^-4) - 5x^-6#
#f'(x) = -1/x^2 + 3/x^4 - 5/x^6#
Let #x = a# be your point. If #f'(a) > 0#, then #f(x)# is increasing at #a#. If #f'(a) < 0#, then #f(x)# is decreasing at #a#.
#f'(-1) = -1/1^2 +3/1^4 - 5/1^6 = -1 + 3 - 5 = -3#
Hence, #f(x)# is decreasing when #x = -1#.

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Answer 2

To determine whether the function f(x) = 1/x - 1/x^3 + 1/x^5 is increasing or decreasing at x = -1, we need to analyze its first derivative at that point. After computing the derivative and evaluating it at x = -1, we find that the first derivative is negative. Therefore, the function is decreasing at x = -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.

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.

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.

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.

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