Question

Is the function f :[3, 4] ➡R defined by f(x) = x^2 -x is a monotonic in its domain

Answer 1

$$f(x)=x^2-x, x\in[3, 4]$$

$$f'(x)=(x^2-x)'=2x-1$$

If $x\in[3, 4],$ then $f'(x)>0$ and $f(x)$ is (strictly) increasing on $[3, 4].$

Therefore the function $f(x)=x^2-x, x\in [3,4]$ is a monotonic in its domain.