Ta có y = |f(x)|, ta tìm max ±f(x) = 16 hoặc min ±f(x) = -16 trên [0, 3]
TH1: [imath]y_1 = f(x) = x^3 - 5x + a[/imath]
[imath]y_1 ' = 3x^2 - 5 = 0 \leftrightarrow x = \sqrt{\cfrac{5}{3}}[/imath]
TH2: [imath]y_2 = -f(x) = -x^3 + 5x - a[/imath]
[imath]y_2 ' = -3x^2 + 5 = 0 \leftrightarrow x = \sqrt{\cfrac{5}{3}}[/imath]
Bảng biến thiên:
[imath]\rightarrow a + 12 = 16,a - \cfrac{10}{3} \sqrt{\cfrac{5}{3}} = -16, -a + \cfrac{10}{3} \sqrt{\cfrac{5}{3}} = 16, -a - 12 = - 16 \newline \rightarrow a = \cfrac{10}{3} \sqrt{\cfrac{5}{3}} - 16, a = 4[/imath]