Question

How to find the two variables that make it differentiable everywhere?

(attached)

Answer 1

so a parabole to a line would mean a sharp turn right?
so that means it wouldn't be differentiable at that point

Answer 2

did yu see the attachement?

Answer 3

yes we have a parabola and then a line that would mean a sharp turn so it wouldn't be differentiable at (-2,13) for any value of a and b

Answer 4

how did yu find that ?

Answer 5

we have f(x)=x^2-4x+1 if x<=-2
so if x=-2
then f(-2)=13

Answer 6

i mean, how do i find value of a and b ?

Answer 7

there is no a and b that would make this function differentiable at x=-2 because there is a sharp turn since we have a parabola to a line
if we were just trying to find a and b such f is continuous on the reals that would be possible

Answer 8

ha! i figured it out hehe

thanks for the hlep

Answer 9

np