Let f be twice–differentiable with f′′(x)>0 for all x in an open interval containing a. For x>a that is still in this interval, which statement describes the relationship between the tangent-line approximation of f(x) at x=a and the actual value f(x)?
a) The approximation overestimates f(x) because the graph is concave up.
b) The approximation underestimates f(x) only when x<a.
c) The approximation underestimates f(x) because the graph is concave up.
d) If f′(a)>0, the approximation overestimates f(x); if f′(a)<0, it underestimates.