Question

Im not sure how to solve this question, i know the answer but idk how to get the answer. Help please!!

Answer 1

if f(x) = 2x, then f ' (x) = ??

Answer 2

2

Answer 3

if g(x) = -x, then g ' (x) = ??

Answer 4

would it be -1?

Answer 5

notice how f ' (x) = 2 while g ' (x) = -1

the two need to be equal at x = 0 in order for the entire piecewise function to be differentiable at x = 0

Answer 6

the derivative graph has a jump discontinuity which means the overall piecewise function is not differentiable at x = 0

Answer 7

Oh ok, so the answer is undefined because there is a jump discontinuity and the values are not equal

Answer 8

there's a jump discontinuity on the derivative graph, yes