[tex]f(x) = - {x}^{8} + 4 {x}^{7} + 8 \\ f'(x) = - 8 {x}^{8 - 1} + 7 \times 4 {x}^{7 - 1} = - 8 {x}^{7} + 28 {x}^{6} \\ - 8 {x}^{7} + 28 {x}^{6} = 0 \\ {x}^{7} - 3.5 {x}^{6} = 0 \\ {x}^{6} (x - 3.5) = 0 \\ x_{1} = 0 \: \: \: \: \: \: \: \: \: x_{2} = 3.5 \\ - - - - [0] + + + + [3.5] - - - - \\ x_{min} = 0 \\ x_{max} = 3.5[/tex]
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[tex]f(x) = - {x}^{8} + 4 {x}^{7} + 8 \\ f'(x) = - 8 {x}^{8 - 1} + 7 \times 4 {x}^{7 - 1} = - 8 {x}^{7} + 28 {x}^{6} \\ - 8 {x}^{7} + 28 {x}^{6} = 0 \\ {x}^{7} - 3.5 {x}^{6} = 0 \\ {x}^{6} (x - 3.5) = 0 \\ x_{1} = 0 \: \: \: \: \: \: \: \: \: x_{2} = 3.5 \\ - - - - [0] + + + + [3.5] - - - - \\ x_{min} = 0 \\ x_{max} = 3.5[/tex]