Question

1D-6
For each of the following functions, find all values of the constants a and b for which the function is differentiable.

f(x) = { x2 + 4x + 1, x ≥ 0;
{ ax + b, x < 0.

what is this question looking for???

Answer 1

See the clips in
http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/1.-differentiation/part-a-definition-and-basic-rules/session-4-limits-and-continuity/

for the background (if you understand limits from the left/right, then you need only review the second clip on Continuity.

The point of your question is a function is differentiable if it's continuous.
You have to make your function continuous.