What is the extreme f(x)=2x^3-27x^2+108x+3 ?

The extreme f(x)=2x^3-27x^2+108x+3 is Maximum(3,138),Minimum(6,111)

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extreme f(x)=2x^3-27x^2+108x+3

extreme points

f (x) = 2 x^{3} - 27 x^{2} + 108 x + 3

Maximum (3, 138), Minimum (6, 111)

Solution steps

f^{'} (x) = 6 x^{2} - 54 x + 108

Find intervals:

Increasing

: - \infty < x < 3,

Decreasing

: 3 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 3

into

2 x^{3} - 27 x^{2} + 108 x + 3 : 138

Maximum (3, 138)

Plug

x = 6

into

2 x^{3} - 27 x^{2} + 108 x + 3 : 111

Minimum (6, 111)

Maximum (3, 138), Minimum (6, 111)

f (x) = - 5 x^{2} + 1630 x

y = \frac{5 - x}{2 x + 6}

f (x) = 3 x^{4} - 7 ln (x)

f (x, y) = ln (9 x^{2} + 3 y^{2} - 4)

f (x) = 3 x^{\frac{2}{3}} - 7

What is the extreme f(x)=2x^3-27x^2+108x+3 ?
The extreme f(x)=2x^3-27x^2+108x+3 is Maximum(3,138),Minimum(6,111)