The interval in which the function $f(x) = 10 - 6x - 2x^2$ is decreasing is :

The interval on which the function $f(x) = x^4 - \frac{x^3}{3}$ is strictly decreasing, is:

If a function $f(x)=x^{2}+b x+1$ is increasing in the interval $[1,2]$, then the least value of $b$ is :

If $y = ax^2 + bx$ has minima at $x = 2$ and the minimum value is -12, then which of the following are correct?

(A) $a = 3$

(B) $a = -3$

(C) $b = 12$

(D) $b = -12$

Choose the correct answer from the options given below:

Let $f(x) = 4x^3 - 18x^2 + 27x - 5$, $x \in R$. Then which of the following statements are TRUE?

(A) $f''(x) = 24x - 36$

(B) f has local maxima at $x = \frac{3}{2}$ but no minima

(C) f has neither maxima nor minima

(D) f has both maxima and minima

Choose the correct answer from the options given below:

An energy DRONE is flying along the curve $y = x^2 + 7$. A soldier is placed at $(3, 7)$. The nearest distance of the DRONE from soldier's position is

The number of tangents to the curve $xy - 3y + 2 = 0$ having slope 2 is: