Critical Point

Q.

Find the critical points of the function $f\left(x\right)=2x^3+15x^2+36x.$

1. x = 2 , x = 3

2. x = - 2 , x = 3

3. x = 2 , x = - 3

4. x = - 2 , x = - 3

Q.

The equation $2^{2x}+(a-1)2^{x+1}+a=0$ has roots reciprocal to each, then set of values of 'a' is

1. 

2. 

3. 

4. a < 0

Q. The set of values of a for which the function $f\left(x\right)=(4a-3)(x+ln5)+2(a-7)cot\left(\frac{x}{2}\right)si{n}^2\left(\frac{x}{2}\right)$ does not possess critical point is

1. $(1,\infty )$
2. $[1,\infty )$
3. $(-\infty ,2)$
4. $(-\infty ,\frac{-4}{3})\cup (2,\infty )$

Q. If m, n are positive integers then ${\int }_u^b{(x-a)}^m{(b-x)}^{n}dx$ equals

1. $\frac{m!n!}{(m+n)!}$
2. $\frac{m!n!{(b-a)}^{m+n}}{(m+n+1)!}$
3. $\frac{m!n!{(b-a)}^{m+n+1}}{(m+n+1)!}$
4. None of these