A function is defined by h(x)= cases ax^ 2 +b,& x<2 (x-2)(a+b)+5,& x 2 cases The…
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A function h is defined by
h(x)={ax2+b,(x−2)(a+b)+5,x<2x≥2
The function is required to be both continuous and differentiable at x=2. Which ordered pair (a,b) satisfies these conditions?
(a) (1,1)
(b) (115,1135)
(c) (75,715)
(d) (1,3)