What is the extreme f(x)=x(20-2x)(16-x),0<x<10 ?

The extreme f(x)=x(20-2x)(16-x),0<x<10 is Maximum(4,576)

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extreme f(x)=x(20-2x)(16-x),0<x<10

extreme points

f (x) = x (20 - 2 x) (16 - x), 0 < x < 10

Maximum (4, 576)

Solution steps

Find the critical points:

x = 4

Domain of

x (20 - 2 x) (16 - x), 0 < x < 10 : 0 < x < 10

Find intervals:

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < 10

Plug the extreme point

x = 4

into

x (20 - 2 x) (16 - x) \Rightarrow y = 576

Maximum (4, 576)

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

f (x, y) = x^{2} + y^{2} - 20 x + 4 y - 10

2 x^{3} + 6 x^{2} - 90 x + 7, - 5 \leq x \leq 6

f (x) = - \frac{5}{4} x^{2} + \frac{5}{2} x + \frac{7}{4}

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

What is the extreme f(x)=x(20-2x)(16-x),0<x<10 ?
The extreme f(x)=x(20-2x)(16-x),0<x<10 is Maximum(4,576)