The slope of the normal to the curve $y = 2x^2$ at $x = 1$ is:

For the function $f(x) = x^x, x > 0$, which of the following are TRUE?

(A) $f'(x) = x^x(1 + \log x)$

(B) $x = e$ is the critical point

(C) $f$ is increasing in $(\frac{1}{e}, \infty)$

(D) $f$ is increasing in $(0, \infty)$

Choose the correct answer from the options given below:

The revenue function is given by $R(x)=150x-2x^2-x^3$, where $x$ is the number of units demanded, then the marginal revenue when 5 units are sold, is :

The slope of normal to the curve $y = kx^2 - 3x + 2$ at $x = \frac{1}{2}$ is 5. The value of 'k' is

The radius of spherical balloon is decreasing at the rate of 0.1cm/sec, the rate at which its volume is decreasing, when its radius is 0.5cm is

The maximum value of the function $f(x) = x^2(60 - x)$ in [20, 80] is:

Interval in which the function $f(x) = 2x^3 - 3x^2 - 12x + 10$ is decreasing is :