What is the extreme f(x)=x(5-x)(8-x),0<x<5 ?

The extreme f(x)=x(5-x)(8-x),0<x<5 is Maximum(2,36)

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extreme f(x)=x(5-x)(8-x),0<x<5

extreme points

f (x) = x (5 - x) (8 - x), 0 < x < 5

Maximum (2, 36)

Solution steps

Find the critical points:

x = 2

Domain of

x (5 - x) (8 - x), 0 < x < 5 : 0 < x < 5

Find intervals:

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < 5

Plug the extreme point

x = 2

into

x (5 - x) (8 - x) \Rightarrow y = 36

Maximum (2, 36)

f (x) = \frac{( x ^{2} + 121 )}{2 x}

f (x) = - 7 + 12 x - 3 x^{2}

2 x^{3} - 6

f (x) = (x^{2} - 7) (x^{2} - 6) (x^{2} + 4)

f (x) = (x - 3)^{\frac{4}{3}}, - 7 \leq x \leq 7

What is the extreme f(x)=x(5-x)(8-x),0<x<5 ?
The extreme f(x)=x(5-x)(8-x),0<x<5 is Maximum(2,36)