Let f be twice differentiable on the interval 3.8≤x≤4.2 with f′′(x)<0 on that interval. Four students use the tabulated values of f to estimate f′(4).
(A) \;(f(4.2)−f(4))/0.2
(B) \;(f(4)−f(3.8))/0.2
(C) \;(f(4.1)−f(3.9))/0.2
(D) \;(f(4.05)−f(3.95))/0.1
Which student’s estimate is most likely to be an overestimate of f′(4)?
a) Student C
b) Student A
c) Student B
d) Student D