The total number of local maxima and local minima of the function

$$f(x) = \left\{ {\matrix{ {{{(2 + x)}^3},} & { - 3 < x \le - 1} \cr {{x^{2/3}},} & { - 1 < x < 2} \cr } } \right.$$ is

Let $$f(x)$$ be differentiable on the interval (0, $$\infty$$) such that $$f(1)=1$$, and $$\mathop {\lim }\limits_{t \to x} {{{t^2}f(x) - {x^2}f(t)} \over {t - x}} = 1$$ for each $$x > 0$$. Then $$f(x)$$ is

If $$\left|f\left(x_{1}\right)-f\left(x_{2}\right)\right| \leq\left(x_{1}-x_{2}\right)^{2}$$, for all $$x_{1}, x_{2} \in$$ $$\mathbb{R}$$. Find the equation of tangent to the curve $$y=f(x)$$ at the point $$(1,2)$$.