# Is #f(x)=x^2-3lnx# increasing or decreasing at #x=1#?

The function

We must compute the function's derivative in order to ascertain whether a function is increasing or decreasing.

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To determine whether ( f(x) = x^2 - 3 \ln(x) ) is increasing or decreasing at ( x = 1 ), we need to check the sign of the derivative of ( f(x) ) at ( x = 1 ).

The derivative of ( f(x) ) is ( f'(x) = 2x - \frac{3}{x} ).

At ( x = 1 ), ( f'(1) = 2(1) - \frac{3}{1} = 2 - 3 = -1 ).

Since the derivative is negative at ( x = 1 ), the function ( f(x) = x^2 - 3 \ln(x) ) is decreasing at ( x = 1 ).

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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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