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

An open-topped box is to be constructed by removing equal squares from each corner of a $3 \text{ m}$ by $8 \text{ m}$ rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box.

Let the set of all positive values of $\lambda$,for which the point of local minimum of the function $f(x) = 1 + x(\lambda^2 - x^2)$ satisfies $\frac{x^2+x+2}{x^2+5x+6} < 0$,be $(\alpha, \beta)$. Then $\alpha^2 + \beta^2$ is equal to:

If $x$ is real,then the minimum value of $\frac{x^2-x+1}{x^2+x+1}$ is

For all $x \in \mathbb{R}$, the minimum value $\frac{1}{3}$ and the maximum value $3$ of $f(x) = \frac{x^2+x+1}{x^2-x+1}$ occur at $l$ and $m$ respectively. Then $l+m$ is equal to:

$A$ YouTube short video is going viral according to the function $f(t) = -2t^3 + 3t^2 + 5$. At what time $t$ (in hours) does the video get the maximum number of shares?