Question

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

Answer 1

The function `f(x)` is decreasing

Explanation:

The domain of `f(x)` is for `x>0` because of `lnx`

To determine if a function is increasing or decreasing, we must calcute the derivative of the function.

Here `f(x)=x^2-3lnx`

So the derivative is `f'(x)=(x^2)'- (lnx)'=2x-3/x`

Then we calculate `f'(1)=2-3=-1`

Therefore `f(x)` is decreasing at `x=1`