Consider the function f: (0,2) → R defined by f(x) = x/2 + 2/x, and the function g(x) by min{f(t)} for 0

Question

Consider the function **$$f$$**: **$$(0,2)$$** → **$$R$$** defined by $$f(x) = \frac{x}{2} + \frac{2}{x}$$, and the function **$$g(x)$$** by **$$\min\{f(t)\}$$** for $$0 < t \le x, \; 0 < x \le 1$$ and $$g(x) = \frac{3}{2} + x$$ for $$1 < x < 2$$. Which statement about **$$g$$** is correct?

Accepted Answer

A. $$g$$ is continuous but not differentiable at $$x = 1$$

Answer

B. $$g$$ is not continuous for all $$x$$ in $$(0,2)$$

Answer

C. $$g$$ is neither continuous nor differentiable at $$x = 1$$

Answer

D. $$g$$ is continuous and differentiable for all $$x$$ in $$(0,2)$$

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