Quadratic equation

(a) f(x) >2
f(x)-2 >0
4x^2 - 7x - (k+2) >0
Discriminant = (-7)^2 - 4(4)(-k-2) < 0
49 + 16(k+2) < 0
k+2 > 49/16
k>17/16

(b) f(x) = 4x^2 - 7x - k
f(x) = 4(x^2 - 7/4 x) - k
=4(x^2 - 7/4 x + (7/8)^2) - k -4(7/8)^2
= 4(x-7/8)^2 -k-49/16
>= -k-49/16 for all x (since (x-7/8)^2 >=0 for all x)
Therefore, f(x) attains its minimum when x = 7/8