For a twice-differentiable function f with f′′(x)<0 on an open interval containing c, which statement about the linearization L(x) of f at x=c is true for x=c sufficiently close to c?
a) L(x) is less than f(x) for all such x (the linearization is an under–estimate).
b) L(x) is greater than f(x) for all such x (the linearization is an over–estimate).
c) L(x) is greater than f(x) for x>c and less than f(x) for x<c. (sign depends on which side of c)
d) L(x)=f(x) only at x=c and is less than f(x) for every other x near c.