Known function f (x) = x? +ax+b, g (x) = (e x) (CX+d), if both curves y = f (x) and y = g (x) pass through point p (0 0,2) and have the same tangent at point p = 4x+2.

(I) find the values of a, b, c and d.

(ii) If x ≥- 2, find the range of k..

Solution: (1). f(0)= b = 2； f '(x)=2x+a，f '(0)= a = 4； So f(x)=x? +4x+2。

g(0)=d=2,g'(x)=(e^x)(cx+2)+(e^x)c； G'(0)=2+c=4 and c=2, so g (x) = (ex) (2x+2) = 2 (ex) (x+1).

(2)。 What is k?