warmup 1 drag the point to a spot on the graph where the graph is non - differentiable. this graph is…

Explanation:

Step1: Recall non - differentiability conditions

A function is non - differentiable at a point if there is a sharp corner, cusp, vertical tangent, or discontinuity. Since the function is continuous everywhere, we focus on sharp corners and vertical tangents.

Step2: Analyze the graph

At the origin (x = 0), the graph has a cusp. The slope of the left - hand side and the right - hand side of the origin approach different values in a non - smooth way.

Step3: Recall continuity definition

A function (y = f(x)) is continuous at a point (x=a) if (\lim_{x\rightarrow a^{-}}f(x)=\lim_{x\rightarrow a^{+}}f(x)=f(a)). For any (x) value on this graph, as we approach (x) from the left and from the right, the function values approach the same value as the function value at that point. There are no jumps, holes, or asymptotes.

Answer:

The graph is non - differentiable at (x = 0). The graph is continuous everywhere because for every (x) value, the left - hand limit, right - hand limit, and the function value at that (x) are equal.