As $$x$$ varies from $$- 1$$ to $$3,$$ which of the following describes the behavior of the function $$f\left( x \right) = {x^3} - 3{x^2} + 1?$$

Given the following statements about a function $$f:R \to R,$$ select the right option:
$$P:$$ If $$f(x)$$ is continuous at $$x = {x_0},$$ then it is also differentiable at $$x = {x_0},$$
$$Q:$$ If $$f(x)$$ is continuous at $$x = {x_0},$$ then it may not be differentiable at $$x = {x_0},$$
$$R:$$ If $$f(x)$$ is differentiable at $$x = {x_0},$$ then it is also continuous at $$x = {x_0},$$

The integral $$\int\limits_0^1 {{{dx} \over {\sqrt {\left( {1 - x} \right)} }}} $$ is equal ________.

The contour on the $$x-y$$ plane, where the partial derivative of $${x^2} + {y^2}$$ with respect to $$y$$ is equal to the partial derivative of $$6y+4x$$ with respect to $$'x',$$ is