Absolute maximum and absolute minimum of f(x)= ln x on [1,2]?

Question

Can somebody help me with this one.

Find the absolute maximum and absolute minimum of $f(x)$ = $ln(x)$ on $[1,2]$.

Answer 1

Hint. $f(x)=\ln x$ is increasing function.

Answer 2

$$f'(x)=\frac{1}{x} > 0 \quad\forall x \in[1,2]$$ Hence the function is increasing in $[1,2]$. By definition of increasing function: if $$x>x+h$$ then $$f(x)>f(x+h)$$

Therefore $f(1)=0$ is the minimum and $f(2)=\ln 2\approx 0.693$ is the maximum.