Find two positive numbers whose sum is $15$ and the sum of whose squares is minimum.

The minimum value of $2x^2 + x - 1$ is

$A$ missile is fired from the ground level and rises $x$ meters vertically upwards in $t$ seconds, where $x = 100t - \frac{25}{2}t^2$. The maximum height reached is: (in $\text{ m}$)

In the interval $(-4, 4)$,the function $f(x) = \int_{-10}^x (t^4 - 4)e^{-4t} dt$ has:

The maximum value of $f(x) = x^2 \log x$ on the interval $[1, e]$ is:

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