The greatest possible value of '$a$' such that the function $f(x) = x^2 + a x + 1$ is always decreasing in the interval [1, 2] is:

Maximum slope of the curve $y = -x^3 + 3x^2 + 9x - 30$ is

Interval in which the function $f$ given by $f(x) = \tan x - 4x$, $x \in (0, \frac{\pi}{2})$ is strictly decreasing is

If a revenue function is given by $R(x) = 2027x - 1013x^2 - 675x^3$, then the marginal revenue function (MR) is:

The function $f(x) = 6 - 6x - 2x^2$

The function $f(x)=17-9x+6x^2-x^3$ is strictly increasing in the interval, is:

The interval, on which the function $f(x) = x^2e^{-x}$ is increasing, is equal to