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 function, $f(x) = x - \frac{1}{x}$ is

For the function $f(x)=x^4-2x^2+5, x\in R$, then which of the following statements are True?

A. $f(x)$ is increasing on $(-\infty,-1)$

B. $f(x)$ is decreasing on $(-\infty,-1)$

C. $f(x)$ is increasing on $(-1,0)\cup(1,\infty)$

D. $f(x)$ is decreasing on $(1,\infty)$

Choose the correct answer from the options given below:

The function $f(x) = 24x^4 - 32x^3 - 96x^2 + 7$ on the interval $\left[-\dfrac{3}{2}, 4\right]$ is :

A. increasing in $(-1,0)$

B. decreasing in $(0,4)$

C. increasing in $(2,4)$

D. decreasing in $\left(-\dfrac{3}{2},-1\right)$

Choose the correct answer from the options given below:

The sides of an equilateral triangle are increasing at the rate of 5 cm/sec. The rate at which the area increases when the side is 20 cm, is

The rate of change of area of a circle with respect to its circumference when radius is 4cm, is

For the function $f(x) = -2x^3 + 3x^2 + 36x - 10$, which of the following is/are true?

(A) $f$ is increasing in $(-\infty, -2)$

(B) $f$ is increasing in $(-2, 3)$

(C) $f$ is decreasing in $(-\infty, -2)$

(D) $f$ is decreasing in $(3, \infty)$

Choose the correct answer from the options given below: