# Is #f(x)=(-2x^3+4x^2-x-2)/(x+3)# increasing or decreasing at #x=-2#?

decreasing at x = -2

We evaluate f'(a) to find out if a function is increasing or decreasing at x = a.

• At x = a, f(x) is increasing if f'(a) > 0.

• At x = a, f(x) is decreasing if f'(a) < 0.

= (-41-32) = -73

f(x) is decreasing at x = -2 because f'(-2) < 0. The graph is represented as (-2x^3+4x^2-x-2)/(x+3) [-10, 10, -5, 5]}.

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To determine if the function f(x) = (-2x^3 + 4x^2 - x - 2) / (x + 3) is increasing or decreasing at x = -2, we need to analyze the sign of the derivative of the function at x = -2. The function is increasing if the derivative is positive at x = -2, and it is decreasing if the derivative is negative at x = -2.

After finding the derivative and evaluating it at x = -2, if the derivative is positive, the function is increasing at x = -2. If the derivative is negative, the function is decreasing at x = -2.

Therefore, we differentiate the function f(x) = (-2x^3 + 4x^2 - x - 2) / (x + 3) and evaluate it at x = -2 to determine if it's increasing or decreasing at that point.

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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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