Rules for Differentiation (Highschool Calculus)

Question

Find the values of a and b so that g(x) is both continuous and differentiable at x=0.

g(x){ ax+b, x > 0

1-x+x2, x (< and/or =) 0

Answer 1

Function values must agree:

left limit is 1

right limit is b

so b=1

derivative is { a if x>0, 2x-1 if x<0

Derivatives must agree:

a = -1 as x-->0

-x + 1 if x>0

1 - x - x^2 if x<=0