1. **Problem Statement:** We are given the function $$y = x \sqrt{4 - x^2}$$ and information about its critical points, concavity, and points of inflection. 2. **Function and Domain:** The function is $$y = x \sqrt{4 - x^2}$$ where the domain is $$-2 \leq x \leq 2$$ because the expression under the square root must be non-negative. 3. **Critical Points:** - Local minimum at $$x = -\sqrt{2}$$ with $$y = -2$$. - Local maximum at $$x = \sqrt{2}$$ with $$y = 2$$. 4. **Concavity:** - Concave up on the interval $$(-2, 0)$$. - Concave down on the interval $$(0, 2)$$. 5. **Points of Inflection:** - At $$x = 0$$, $$y = 0$$. 6. **Graph Description:** The graph is a curve centered around the origin, shaped by the product of $$x$$ and the square root of $$4 - x^2$$. This function can be graphed to visualize these features clearly.