If g is the function defined above, then g'(3) is...?

Question

g(x) = { 3-x for x<3

4x-12 for x≥3

If g is the function defined above, then g'(3) is...?

A) -1

B) 0

C) 4

D) nonexistent

Answer 1

Approaching from the left the slope of the tangent line at x = 3 is d/dx (3-x) = -1

Approaching from the right the slope is d/dx (4x-12) = 4

As these are not the same the derivative at x=3 doesnt exist so D