The interval in which the function $f(x) = -x^2 - 2x + 18$ is decreasing is :

The total revenue received from the sale of $x$ units of a product is given by $R(x)=24x+5x^2+3$. The marginal revenue when $x=10$ is,

For the function $f(x) = e^{-2x}(2-x)^2$, the point of local maxima is:

If the maximum value of the function $f(x) = \frac{\log_ex}{x}$, $x > 0$ occurs at $x = a$, then $a^2f''(a)$ is equal to

The rate of change in area of a triangle having sides 10 cm and 12 cm when the variable angle between them is $\theta = 60°$, is :

The function $f(x) = kx^3 + 6kx^2 + 18x + 17$ is increasing on $\mathbb{R}$(set of real numbers) if:

The interval in which the function $f(x) = 2x^3 + 3x^2 - 12x + 1$ is strictly increasing, is