Solving for m and b in a differentiable function at x=2.

[Rasine]

f(x)= x^4 x less than or = 2
mx+b x is greater than 2

Find the values of m and b that make f differentiable everywhere.

so what i was trying to do was to find where the graph of x^4=mx where x=2 so that the mx+b function would start at where ever x^4 left off at x=2

i got m=8 and b=0...but that is not right...please tell me what i am doing wrong

 

[mathman]

At x=2:
x⁴=16
4x³=32

Therefore:
2m+b=16
m=32
resulting in b=-48.

 

[Rasine]

thank you so much!