Find a and b such that the function is differentiable everywhere
x^2-2x+1 if x≤3
f(x)= ax+b if x3
a=?
b=?

Question

Find a and b such that the function is differentiable everywhere
          x^2-2x+1   if x≤3
f(x)=  ax+b           if x>3
a=?
b=?

tkhunny · Answer

Why not make it continuous first, and then calculate the one-sided derivatives?

emac · Answer

What I did is I found what f(3) was: 4=a3+b
then I found the derivative: 2x-2=ax+b
and then i found f'(3) which was 16=a3+b
then when I put f(3) and f'(3) together and canceled out I got b=12 but that's the wrong answer
@tkhunny

tkhunny · Answer

The derivative of ax+b is NOT ax+b.

tkhunny · Answer

f(3) = 4 -- That's good.
f'(x) = 2x-2 -- That's good.
f'(3) = 2(3)-2 = 6-2 = 4 -- Where did you get 16?

emac · Answer

Oh I must have still been applying the sq from the original equation instead of just 2(3)-1. So a=4, but where should I plug that in to get B?

emac · Answer

Oh nevermind I got it! I was putting in 8 instead of -8. Thank you!!