What is the extreme f(x)=12x-9x^2+2x^3 ?

The extreme f(x)=12x-9x^2+2x^3 is Maximum(1,5),Minimum(2,4)

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extreme f(x)=12x-9x^2+2x^3

extreme points

f (x) = 12 x - 9 x^{2} + 2 x^{3}

Maximum (1, 5), Minimum (2, 4)

Solution steps

f^{'} (x) = 12 - 18 x + 6 x^{2}

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 1

into

12 x - 9 x^{2} + 2 x^{3} : 5

Maximum (1, 5)

Plug

x = 2

into

12 x - 9 x^{2} + 2 x^{3} : 4

Minimum (2, 4)

Maximum (1, 5), Minimum (2, 4)

f (x, y) = 5 x^{2} - 4 x y + 4 y^{2} + 12 x + 25

f (x) = 2 x^{3} - \frac{12 x ^{2}}{2} - 2 [- 1.3]

\frac{27 x ^{2}}{( 2 - x ) ^{3}}

\frac{8 x ^{2}}{x - 6}, - 3 \leq x \leq 2

f (x, y) = x + 3 y

What is the extreme f(x)=12x-9x^2+2x^3 ?
The extreme f(x)=12x-9x^2+2x^3 is Maximum(1,5),Minimum(2,4)