The sum of the absolute maximum and minimum values of the function $f(x) = |x^2 - 5x + 6| - 3x + 2$ in the interval $[-1, 3]$ is equal to:

The area bounded by the tangents of the curve given by $y = \sin \theta \cos^2 \theta$ and $x = \sin^2 \theta \cos \theta$,which are parallel to the coordinate axes (excluding the axes themselves),is:

$P(x) = x^4 + ax^3 + bx^2 + cx + d$ is such that $x = 0$ is the only real root of $P'(x) = 0$. If $P(-1) < P(1)$,then in the interval $[-1, 1]$:

Find the absolute maximum of $x^{40}-x^{20}$ on the interval $[0,1]$.

The absolute maximum value of $f(x) = \sin x + \cos x$ for $x \in [0, \pi]$ is . . . . . . .

Let $f(x) = 1 - \sqrt{x^2}$,where the square root is to be taken as positive. Then: