The sum of the maximum and minimum values of the function $f(x)=\frac{x^2-x+1}{x^2+x+1}$ is

Find the absolute maximum and minimum values of a function $f$ given by $f(x) = 2x^{3} - 15x^{2} + 36x + 1$ on the interval $[1, 5]$.

The curve $y(x) = ax^{3} + bx^{2} + cx + 5$ touches the $x$-axis at the point $P(-2, 0)$ and cuts the $y$-axis at the point $Q$,where the derivative $y'(0) = 3$. Find the local maximum value of $y(x)$.

The maximum slope of the curve $y=-x^{3}+3x^{2}+2x-27$ is

Let $M$ and $m$ be respectively the local maximum and the local minimum values of the function $f(x) = 2x^3 - 9x^2 + 12x + 5$ in the interval $[0, 3]$. Then $M - m$ is equal to

Let a function $f(x)$ be defined as $f(x) = \begin{cases} \cos^{-1}(\mu) + x^2, & 0 < x < 1 \\ 4x, & x \geqslant 1 \end{cases}$. The function $f(x)$ can have a local minimum at $x = 1$ if the value of $\mu$ lies in the interval: