extreme 11x^2+2*(-25)x(1-x)+24(1-x)^2

解答

极值点

11 x^{2} + 2 \cdot (- 25) x (1 - x) + 24 (1 - x)^{2}

极小值 (\frac{49}{85}, - \frac{361}{85})

求解步骤

f^{'} (x) = 170 x - 98

Find intervals:

递减

: - \infty < x < \frac{49}{85},

递增

: \frac{49}{85} < x < \infty

将

x = \frac{49}{85}

代入

11 x^{2} + 2 \cdot (- 25) x (1 - x) + 24 (1 - x)^{2} : - \frac{361}{85}

极小值 (\frac{49}{85}, - \frac{361}{85})

e x t re m e f (x, y) = x^{2} + y^{2} + \frac{16}{x} + \frac{2}{y}

e x t re m e f (x) = - 5 x^{4} - 5 x^{3} - 2

e x t re m e f (x) = - x^{3} - 6 x^{2} - 1

e x t re m e f (x) = \frac{x ^{2} - 4}{x ^{2} + 4}, - 5 \leq x \leq 5

e x t re m e y = - 4 x^{2} - 5 x + 1