Question

Solve for a and b...

Answer 1

f is continuous for all f E R

(a - b)x - 2 if x < 3
f(x) = 4a + b if x = 3
-bx + 2a if x > 3

1) Solve for a and b
2) Is f(x) differentiable at x = 3
Show all the necessary calculations to explain your answer

Answer 2

My notation wasn't very clear so here is the original

Answer 3

Note that f(x) is continuous, which mean there is no any kind of discontinuous, such as jump discontinuity

So that mean \((a-b)x-2~=~4a+b~=~-bx+2a\) at \(x=3\)

So just plug in 3 for x then solve for a and b

Answer 4

Thank you! I managed to solve it with your help!

Answer 5

glad I helped. do you also need help with 2.2?