If the interval in which the function $f(x) = 4x^3 - 6x^2 - 72x + 30$ is strictly decreasing, is (a,b) then a+b is equal to

A steel plant is capable of producing 'x' tonnes per day of low-grade steel and 'y' tonnes per day of high-grade steel, where $y=\frac{32-5x}{10-x}$. If the fixed price of low-grade steel is half that of high-grade steel, then the quantity of low-grade steel that should be produced per day for maximum receipts is

Match List-I with List-II

Consider the function f(x) = 2x³ - 21x² + 36x + 80, x∈[0, 6]. Then

Choose the correct answer from the options given below:

The function $f: R \rightarrow R$ (where $R$ is set of real numbers) defined as

$f(x) = x^2 + 2x$ is

The function $f(x) = x^2e^{-2x}$ increases on

The appropriate change in the volume V of a cube of side $x$ metres caused by increasing the side by 2% is :

For the function $f(x) = (x+1)^2(x-2)^2$, which of the following statements are TRUE?

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

(B) $f(x)$ is increasing on $\left(-1,\frac{1}{2}\right)$

(C) $f(x)$ is decreasing on $\left(\frac{1}{2},2\right)$

(D) $f(x)$ is increasing on $(2,\infty)$

Choose the correct answer from the options given below: