The demand function of a monopolist is given by $p = 1500 - 2x - x^2$, then value of marginal revenue when $x = 20$ is :

If $x = 2t^2 + 3, y = 3t^2 + 6t + 5$, then the value of $\frac{d^2y}{dx^2}$ is :

If $y = x^3 \log x$, then $\frac{d^2 y}{dx^2}$ is equal to :

The value of the integral $\int_{-3}^{3} (x^3 - x) dx$ is :

If $x^{2/3} + y^{2/3} = a^{2/3}$, then $\frac{dy}{dx}$ is equal to :

If $C(x) = ax^2 - bx - c$ represents the total cost function then the slope of the tangent to the marginal cost curve at the point $(x, y)$ is :

The interval in which where the function $f(x) = x^3 - 3x^2 + 4x + 1, x \in R$ is increasing in, is :