If the absolute maximum and absolute minimum values of the function $f(x) = x^3 - 2x^2 + x - 3$ defined on $[0, 2]$ are $M$ and $m$ respectively, then $M + m =$

If $f(x) = \sin x - x \cos x$ has a maximum at $x = n\pi$,then which of the following is true?

The curvilinear trapezoid is bounded by the curve $y = x^2 + 1$ and the straight lines $x=1$ and $x=2$. The coordinates of the point $(x_1, y_1)$ on the given curve with abscissa $x_1 \in [1, 2]$,where the tangent drawn cuts off an ordinary trapezium of the greatest area from the curvilinear trapezoid,are

What is one of the maximum values of $f(x) = x + \sin(2x)$ in the interval $[0, 2\pi]$?

The function $f(x) = x\sqrt{1 - x^2}$ for $x > 0$ has:

The minimum value of $\frac{\log x}{x}$ in the interval $[2, \infty)$ is