What is the extreme 11x^2+2*(-25)x(1-x)+24(1-x)^2 ?

The extreme 11x^2+2*(-25)x(1-x)+24(1-x)^2 is Minimum(49/85 ,-361/85)

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

extreme points

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

Minimum (\frac{49}{85}, - \frac{361}{85})

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Plug

x = \frac{49}{85}

into

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

Minimum (\frac{49}{85}, - \frac{361}{85})

f (x, y) = x^{2} + y^{2} + \frac{16}{x} + \frac{2}{y}

f (x) = - 5 x^{4} - 5 x^{3} - 2

f (x) = - x^{3} - 6 x^{2} - 1

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

f (x) = 7 x^{2} - 56 x + 84

What is the extreme 11x^2+2*(-25)x(1-x)+24(1-x)^2 ?
The extreme 11x^2+2*(-25)x(1-x)+24(1-x)^2 is Minimum(49/85 ,-361/85)