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## Homework Statement

For all real numbers a and b, define g(x) = 3x² if x≤1, a+bx if x>1. For what values of a and b is g differentiable at x=1?

## Homework Equations

## The Attempt at a Solution

g(x) is continuous: lim as x→1- [f(x)] = 1; lim as x→1+ [f(x)] = a+b

g(x) is differentiable: g'(x) = lim as x→1- of [(g(x)-g(1))/x-1] = 6 and g'(x) = lim as x→1+ [(g(x)-g(1))/x-1]=lim as x→1+ (b) = 0 {I think the limit from the right is correct}

I believe a=6, and I am not sure what b equals.