Cho các số thực a, b, c, d thỏa mãn 0

* Hướng dẫn giải

Đáp án C

Dựa vào đồ thị hàm số suy ra bảng biến thiên

$\Rightarrow \left\{\begin{array}{l}M=\left\{f\left(0\right),f\left(b\right),f\left(d\right)\right\}\\ m=\left\{f\left(a\right),f\left(c\right)\right\}\end{array}\right.$

- Mặt khác dựa vào đồ thị hàm số, ta thấy rằng 

+  $\underset{a}{\overset{b}{\int }}{f}^{\text{'}}\left(x\right)dx<\underset{b}{\overset{c}{\int }}\left[-f^{\text{'}}\left(x\right)\right]dx\Rightarrow f\left(x\right)\left|\begin{array}{l}{}^b\\ {}_c\end{array}\right.-f\left(x\right)\left|\begin{array}{l}{}^c\\ {}_b\end{array}\right.\iff f\left(a\right)>f\left(c\right)$

+  $\underset{0}{\overset{a}{\int }}\left[-f^{\text{'}}\left(x\right)\right]dx>\underset{a}{\overset{b}{\int }}{f}^{\text{'}}\left(x\right)dx\iff f\left(0\right)-f\left(a\right)>f\left(b\right)-f\left(a\right)\iff f\left(0\right)>f\left(b\right)$

+  $\underset{c}{\overset{b}{\int }}\left[-f^{\text{'}}\left(x\right)\right]dx>\underset{c}{\overset{d}{\int }}{f}^{\text{'}}\left(x\right)dx\iff f\left(b\right)-f\left(c\right)>f\left(d\right)-f\left(c\right)\iff f\left(b\right)>f\left(d\right)$

Vậy $\left\{\begin{array}{l}f\left(a\right)>f\left(c\right)\Rightarrow m=f\left(c\right)\\ f\left(0\right)>f\left(b\right)>f\left(d\right)\Rightarrow M=f\left(0\right)\end{array}\right.\Rightarrow M+m=f\left(0\right)+f\left(c\right)$