A network uses the custom activation
g(x)={3x−1x<2x2+cx≥2g(x) = \begin{cases} 3x - 1 & x < 2 \\[4pt] x^2 + c & x \ge 2 \end{cases}g(x)={3x−1x2+cx<2x≥2
where ccc is a constant the designer gets to pick. Training needs a derivative to exist at every input the function meets.
Which statement is true?
Select all that apply.
c=1c = 1c=1, and with that value ggg is differentiable at x=2x = 2x=2.
c=5c = 5c=5 makes ggg continuous at x=2x = 2x=2, but ggg is not differentiable there.
c=1c = 1c=1 makes ggg continuous at x=2x = 2x=2, but ggg is still not differentiable there.
c=−1c = -1c=−1, and with that value ggg is both continuous and differentiable at x=2x = 2x=2.