The equation of tangent line to $y = 2x^2 + 7$, which is parallel to the line $4x - y + 3 = 0$ is

If the function $f(x) = x^2 - ax - 2$ is strictly decreasing on $(2, 3)$ then $a$ lies in the interval.

The total revenue received from the sale of $x$ units of a product is given by $R(x)=542+\dfrac{x^2+3}{4}$. What will be the marginal revenue when $x=24$ ?

The interval for which the function $f(x)=\frac{x}{x^2+x+1}$ is an increasing function, is:

The maximum slope of the tangents to the curve $y(x) = -x^3 + 3x^2 + 9x - 30$ is

The function $f(x) = 4x^3 - 7x^2$ has point(s) of local minima at

The slope of the normal to the curve $y = 2x^2 - 4$ at P (1, -2) is :