At x = 1, the function $f(x)=x^4-48x^2+\alpha x+120$ attains its maximum value in the interval [0, 2], then the value of $\alpha$ is:

Which of the following statements are correct ?

A. The function $f(x) = a^x$ is increasing on $(-\infty,\infty)$ if $a>1$.

B. $f(x) = x^2 - 2x$ is decreasing in $(-\infty,1)$.

C. $f(x) = x(x-3)^2$ increases for $1 \le x \le 3$.

D. $f(x) = e^{-x}$ decreases in $[0,\infty)$.

Choose the correct answer from the options given below:

The absolute maximum value of the function $f(x) = \frac{x}{2} + \frac{2}{x}$ in the interval $[-3, 3]$, is

If the total cost function is given by $C(x)=\frac{x^3}{3}-2x^2+9x-70$ and the selling price per unit is ₹6, then for what value of $x$ will the profit be maximum?

For the function $f(x)=2x^3-21x^2+36x-100$;

Match the LIST-I with LIST-II

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If a revenue function is given by $R(x) = 2027x - 1013x^2 - 675x^3$, then the marginal revenue function (MR) is:

Based on above information answer the following question :

If area of the flower bed is maximum, then area (in $m^2$) of the garden, which is outside the flower bed is :