What is the extreme f(x)=2x^3-12x^2+18x-5 ?

The extreme f(x)=2x^3-12x^2+18x-5 is Maximum(1,3),Minimum(3,-5)

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extreme f(x)=2x^3-12x^2+18x-5

extreme points

f (x) = 2 x^{3} - 12 x^{2} + 18 x - 5

Maximum (1, 3), Minimum (3, - 5)

Solution steps

f^{'} (x) = 6 x^{2} - 24 x + 18

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 1

into

2 x^{3} - 12 x^{2} + 18 x - 5 : 3

Maximum (1, 3)

Plug

x = 3

into

2 x^{3} - 12 x^{2} + 18 x - 5 : - 5

Minimum (3, - 5)

Maximum (1, 3), Minimum (3, - 5)

x^{2} + 4 x y + y^{2}

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

x + 2

f (x, y) = 80 x + 80 y - x^{2} - y^{2}

f (x) = x^{2} + \frac{800}{x}

What is the extreme f(x)=2x^3-12x^2+18x-5 ?
The extreme f(x)=2x^3-12x^2+18x-5 is Maximum(1,3),Minimum(3,-5)