TIFR ECE 2020 | Question: 4

Question

Let $f, g: \mathbb{R} \rightarrow \mathbb{R}$ be two functions that are continuous and differentiable. Consider the following statements:

1. $\min \{f, g\}$ is continuous
2. $\max \{f, g\}$ is continuous
3. $\max \{f, g\}$ is differentiable

Which of the following is $\text{TRUE?}$

• A. Only statement $1$ is correct
• B. Only statement $2$ is correct
• C. Only statement $3$ is correct
• D. Only statements $1$ and $2$ are correct
• E. None of the above