Sufficient Condition for an Extrema

Q. $20$ is divided in two parts so that product of cube of one quantity and square of other quantity is maximum.The parts are-

1. $10,10$
2. $16,4$
3. $12,8$
4. $6,14$

Q. The point of inflection for the function $f\left(x\right)={\sin }^{-1}x$ is:

1. $x=\frac{1}{2}$
2. $x=\frac{1}{\sqrt{2}}$
3. $x=-\frac{1}{2}$
4. $x=0$

Q.

f(x) and f’(x) are differentiable at x = c. A sufficient condition for f(c) to be an extremum of f(x) is that f’(x) changes sign as x passes through c

1. True

2. False