What is the extreme f(x)=x(14-2x)(15-x) ?

The extreme f(x)=x(14-2x)(15-x) is Maximum(3,288),Minimum(35/3 ,-9800/27)

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extreme f(x)=x(14-2x)(15-x)

extreme points

f (x) = x (14 - 2 x) (15 - x)

Maximum (3, 288), Minimum (\frac{35}{3}, - \frac{9800}{27})

Solution steps

f^{'} (x) = 2 (x - 3) (3 x - 35)

Find intervals:

Increasing

: - \infty < x < 3,

Decreasing

: 3 < x < \frac{35}{3},

Increasing

: \frac{35}{3} < x < \infty

Plug

x = 3

into

x (14 - 2 x) (15 - x) : 288

Maximum (3, 288)

Plug

x = \frac{35}{3}

into

x (14 - 2 x) (15 - x) : - \frac{9800}{27}

Minimum (\frac{35}{3}, - \frac{9800}{27})

Maximum (3, 288), Minimum (\frac{35}{3}, - \frac{9800}{27})

\frac{1}{4} x^{4} - \frac{2}{3} x^{3} - \frac{1}{2} x^{2} + 2 x - 1

f (x) = 2 x^{2} + 3 y^{2} - 7

f (x) = \frac{1}{3} x^{3} - x^{2} + x - 5

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

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

What is the extreme f(x)=x(14-2x)(15-x) ?
The extreme f(x)=x(14-2x)(15-x) is Maximum(3,288),Minimum(35/3 ,-9800/27)