Suppose $f$ Is a Piecewise-Defined Function, Equal To $g ( x ) \text { if } x < 3 \text {, and } h ( x ) \text { if } x \geq 3 \text {, }$

True/False

Suppose $f$ is a piecewise-defined function, equal to $g ( x ) \text { if } x < 3 \text {, and } h ( x ) \text { if } x \geq 3 \text {, }$ where $g \text { and } h$ are continuous and differentiable everywhere. If $g ^ { \prime } ( 3 ) = h ^ { \prime } ( 3 )$ is the function $f$ differentiable at $x = 3 ?$ Explain why or why not.