If f(x) is differentiable, then what is the values of b?

Question

f(x) =

1. 5x + ax^4, x > 2
2. bx^2 - 3x, x ≤ 2

Answer 1

The function must be continuous to be differentiable.

That means the first part of the function at x=2 has to = the second part at x=2, even though the first part isn't defined at exactly x=2.

5(2)+a(2)^4 = b(2)^2 - 3(2)

10 + 16a = 4b -6

16+16a = 4b

4 + 4a = b