Find the values of m and b that make the following function differentiable.

Question

Answer 1

The slope at x=2 must be 4 (i.e. 2x); therefore m=4.

The straight line must go through (2,4), i.e. 4=4*2 + b so that b=-4.

Answer 2

The function must be continuous at x = 2, so 2² = 2m + b. Thus, 2m + b = 4.

The one sided derivatives must also be equal when x = 2. So, 2x = m when x = 2.

Therefore, m = 4 and b = -4.