The function $f(x) = 2x^3 - 3x^2 - 36x + 7$ is :

A. Increasing in $(-\infty,-2)$

B. Decreasing in $(-2,3)$

C. Neither increasing nor decreasing in $(-2,3)$

D. Increasing in $(3,\infty)$

Choose the correct answer from the options given below:

The line $ax + by = 7$ is a tangent to the curve $y = \frac{x-7}{(x-2)(x-3)}$ at the point where it cuts the x-axis

A. The y-intercept of the line is $-0.7$

B. $b = -7$

C. $a = 1$

D. the line passes through the point $(-13, -1)$

E. $b = -20$

Choose the correct answer from the options given below:

The maximum value of the function $f(x)=\sin x(1+\cos x)$ in the internal $[0,\pi]$ is

If $f(x) = a \log_e|x| + bx^2 + x$ has critical points at $x = -2$ and $x = 1$, then

The maximum value of $2x^3 - 24x + 107$ in the interval $[1, 3]$ is :

For the function $f(x) = \dfrac{3}{2}x^4 - 4x^3 - 45x^2 + 49$. Which of the following statements is/are TRUE ?

A. $f(x)$ is increasing in $(-\infty, -3)$

B. $f(x)$ is increasing in $(-3, 0) \cup (5, \infty)$

C. $f(x)$ is decreasing in $(-\infty, -3) \cup (0, 5)$

D. $f(x)$ is decreasing in $(-\infty, -3) \cup (5, \infty)$

Choose the correct answer from the options given below:

Based on above information answer the following question :

The maximum area (in $m^2$) of the flower bed is :