What is the extreme y=x(10-2x)(8-x) ?

The extreme y=x(10-2x)(8-x) is Maximum(2,72),Minimum(20/3 ,-800/27)

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extreme y=x(10-2x)(8-x)

extreme points

y = x (10 - 2 x) (8 - x)

Maximum (2, 72), Minimum (\frac{20}{3}, - \frac{800}{27})

Solution steps

f^{'} (x) = 2 (x - 2) (3 x - 20)

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < \frac{20}{3},

Increasing

: \frac{20}{3} < x < \infty

Plug

x = 2

into

x (10 - 2 x) (8 - x) : 72

Maximum (2, 72)

Plug

x = \frac{20}{3}

into

x (10 - 2 x) (8 - x) : - \frac{800}{27}

Minimum (\frac{20}{3}, - \frac{800}{27})

Maximum (2, 72), Minimum (\frac{20}{3}, - \frac{800}{27})

f (x) = \frac{3 x ^{2} - 16 x + 16}{( x ^{2} - 2 x ) ^{2}}

- x^{\frac{2}{3}} (x - 5)

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

f (x, y) = x + 2 y - 2 x y - x^{2} - 3 y^{2}

What is the extreme y=x(10-2x)(8-x) ?
The extreme y=x(10-2x)(8-x) is Maximum(2,72),Minimum(20/3 ,-800/27)