What is the extreme y=x(20-2x)(16-x) ?

The extreme y=x(20-2x)(16-x) is Maximum(4,576),Minimum(40/3 ,-6400/27)

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extreme y=x(20-2x)(16-x)

extreme points

y = x (20 - 2 x) (16 - x)

Maximum (4, 576), Minimum (\frac{40}{3}, - \frac{6400}{27})

Solution steps

f^{'} (x) = 2 (x - 4) (3 x - 40)

Find intervals:

Increasing

: - \infty < x < 4,

Decreasing

: 4 < x < \frac{40}{3},

Increasing

: \frac{40}{3} < x < \infty

Plug

x = 4

into

x (20 - 2 x) (16 - x) : 576

Maximum (4, 576)

Plug

x = \frac{40}{3}

into

x (20 - 2 x) (16 - x) : - \frac{6400}{27}

Minimum (\frac{40}{3}, - \frac{6400}{27})

Maximum (4, 576), Minimum (\frac{40}{3}, - \frac{6400}{27})

y = e^{x} + 1

f (x) = x^{3} - 6 x + 6

f (x) = 12 x^{3} - 24 x^{2} + 12 x

f (x, y) = cos^{2} (t) \cdot sin^{2} (t)

What is the extreme y=x(20-2x)(16-x) ?
The extreme y=x(20-2x)(16-x) is Maximum(4,576),Minimum(40/3 ,-6400/27)