Necessary Condition for an Extrema(Is a Function Differentiable at Boundaries)

Q. f(x) = sin¯¹ [2x] + cos¯¹([x]-1). Domain of function=[a, b) and range= {c, d} then a+b+2(d/c)=?

Q. Suppose $f\left(x\right)=x^3+a{x}^2+bx+c$ satisfies $f(–2)=-10$ and takes the extreme value $\frac{50}{27}$ at $x=\frac{2}{3}.$ Then the value of $a+b+c$ is