Let $f : \mathbb { R } \rightarrow \mathbb { R }$ be a function, where $\mathbb { R }$ is the set of real numbers. For each statement below, write whether it is TRUE or FALSE. a) If $| f ( x ) - f ( y ) | \leq 39 | x - y |$ for all $x , y$ then $f$ must be continuous everywhere. Answer: $\_\_\_\_$ b) If $| f ( x ) - f ( y ) | \leq 39 | x - y |$ for all $x , y$ then $f$ must be differentiable everywhere. Answer: $\_\_\_\_$ c) If $| f ( x ) - f ( y ) | \leq 39 | x - y | ^ { 2 }$ for all $x , y$ then $f$ must be differentiable everywhere. Answer: $\_\_\_\_$ d) If $| f ( x ) - f ( y ) | \leq 39 | x - y | ^ { 2 }$ for all $x , y$ then $f$ must be constant. Answer: $\_\_\_\_$
Let $f : \mathbb { R } \rightarrow \mathbb { R }$ be a function, where $\mathbb { R }$ is the set of real numbers. For each statement below, write whether it is TRUE or FALSE.\\
a) If $| f ( x ) - f ( y ) | \leq 39 | x - y |$ for all $x , y$ then $f$ must be continuous everywhere.
Answer: $\_\_\_\_$\\
b) If $| f ( x ) - f ( y ) | \leq 39 | x - y |$ for all $x , y$ then $f$ must be differentiable everywhere.
Answer: $\_\_\_\_$\\
c) If $| f ( x ) - f ( y ) | \leq 39 | x - y | ^ { 2 }$ for all $x , y$ then $f$ must be differentiable everywhere.
Answer: $\_\_\_\_$\\
d) If $| f ( x ) - f ( y ) | \leq 39 | x - y | ^ { 2 }$ for all $x , y$ then $f$ must be constant.
Answer: $\_\_\_\_$