Consider the function f:(0,2)→R defined by f(x)=2x+x2 and the function g(x) defined by g(x)={\begin{matrix}\text{min}{f(t)}, & 0<t\leq x\text{ and }0<x\leq 1 \\ \frac{3}{2}+x, & 1<x<2\end{matrix}. Then
Held on 27 Jan 2024 · Verified 6 Jul 2026.
g is continuous but not differentiable at x=1
g is not continuous for all x∈(0,2)
g is neither continuous nor differentiable at x=1
g is continuous and differentiable for all x∈(0,2)
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