f(x) = { (x) + 8, x < 4 and { 4x +6, x 4

For part one: Is f(x) continuous at x = 4?

For a function to be considered continuous, the left and right hand limits should be equal. For the left hand limit, we take (x) + 8 and we plug in the 4. That gives us (4) + 8, which simplifies to 10. Next, we want to take a look at the right hand limit. Just like with our first limit, we take 4x +6 and plug in 4 for the x. This gives us 4(4) +6 which simplifies to 10. Thus, our left and right hand limits are both equal to 10, making the function continuous at x = 4.

For part two: Is f(x) differentiable at x = 4?