The function $f(x)=\frac{x}{\sin x}$ is strictly increasing in the interval.

For what values of the parameter ' $a$ ' does the function $f(x)=x^3+3(a-7) x^2+3\left(a^2-9\right) x-1$ have a positive point of maximum.

The slope of the curve $2 y^2=a x^2+b$ at $(1,-1)$ is -1 . Then, the value of $b$ is

The maximum area of rectangle inscribed in a circle of diameter $ R $ is