The maximum value of $f(x) = (7-x)^4 (2+x)^5$ is

The maximum area of a parallelogram inscribed in a triangle $ABC$ (given that $A$ is also one of the vertices of the parallelogram) is equal to (where symbols have their usual meaning in $\Delta ABC$):

$x^x$ has a stationary point at

If $f(x) = x^5 - 5x^4 + 5x^3 - 10$ has local maximum and minimum at $x = p$ and $x = q$,respectively,then $(p, q)$ equals

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

If $\frac{dy}{dx} = (x - 1)^3 (x - 2)^4$,then $y$ has: