the function f is twice differentiable, and the graph of f has no points of inflection.if f(6)=3,

Question

f'(6)=-1/2,and f''(6)=-2,which of the following could be the value of f(7)?
a.2 b.2.5 c.2.9 d.3 e.4
答案是a,有没有合理的解释?

Answer 1

f'(6)=-1/2=>f(7)<f(6)
故答案在a,b,c中
the graph of f has no points of inflection并且f''(6)=-2 =>
f'(6+dx)<f'(x)
那么f(7)<f(6)+(7-6)f'(6)=3-0.5=2.5
故只有a是有可能的值