Is #f(x)=3x^3-6x-7 # increasing or decreasing at #x=0 #?
decreasing at x = 0
Finding f'(x) and evaluating f'(0) are necessary to determine whether the function is increasing or decreasing at x = 0.
• At x = 0, f(x) is increasing if f'(0) > 0.
• At x = 0, f(x) is decreasing if f'(0) < 0.
and f'(0) = - 6 < 0
Thus, at x = 0, f(x) is decreasing.
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To determine if the function f(x) = 3x^3 - 6x - 7 is increasing or decreasing at x = 0, we examine the sign of its derivative at that point. Calculate the derivative of f(x) with respect to x, which is f'(x) = 9x^2 - 6. Then, substitute x = 0 into the derivative function to find the sign of the derivative at x = 0. Since f'(0) = -6 < 0, the function is decreasing at x = 0.
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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.
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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