BBT hàm f(x)
Từ BBT ta thấy \(\max\limits_{\left[-1;3\right]}f\left(x\right)=f\left(1\right)\Rightarrow b=1\)
Đồng thời ta thấy: \(\left\{{}\begin{matrix}f\left(1\right)>f\left(0\right)\\f\left(1\right)>f\left(2\right)\end{matrix}\right.\)
Từ giả thiết:
\(f\left(-1\right)+f\left(0\right)-2f\left(1\right)=f\left(3\right)-f\left(2\right)\)
\(\Leftrightarrow f\left(-1\right)-f\left(3\right)=\left[f\left(1\right)-f\left(2\right)\right]+\left[f\left(1\right)-f\left(0\right)\right]>0\)
\(\Rightarrow f\left(-1\right)>f\left(3\right)\)
\(\Rightarrow\min\limits_{\left[-1;3\right]}f\left(x\right)=f\left(3\right)\Rightarrow a=3\)
\(\Rightarrow a+b=4\)
