# Suppose #g# is a function whose derivative is #g'(x)=3x^2+1# Is #g# increasing, decreasing, or neither at #x=0#?

Increasing

Another approach,

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To determine if the function g is increasing, decreasing, or neither at x = 0, we can analyze the sign of the derivative g'(x) at x = 0.

Substitute x = 0 into g'(x) to find g'(0): g'(0) = 3(0)^2 + 1 = 0 + 1 = 1

Since g'(0) is positive (1), the function g is increasing 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.

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