What is the extreme f(x)=x^3-4x^2+5x-2 ?

The extreme f(x)=x^3-4x^2+5x-2 is Maximum(1,0),Minimum(5/3 ,-4/27)

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extreme f(x)=x^3-4x^2+5x-2

extreme points

f (x) = x^{3} - 4 x^{2} + 5 x - 2

Maximum (1, 0), Minimum (\frac{5}{3}, - \frac{4}{27})

Solution steps

f^{'} (x) = 3 x^{2} - 8 x + 5

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < \frac{5}{3},

Increasing

: \frac{5}{3} < x < \infty

Plug

x = 1

into

x^{3} - 4 x^{2} + 5 x - 2 : 0

Maximum (1, 0)

Plug

x = \frac{5}{3}

into

x^{3} - 4 x^{2} + 5 x - 2 : - \frac{4}{27}

Minimum (\frac{5}{3}, - \frac{4}{27})

Maximum (1, 0), Minimum (\frac{5}{3}, - \frac{4}{27})

f (x) = - 2 x + 5

(1 - 3) (7 - 2)

(2.7) (10.16)

f (x) = \frac{( 4 x - 1 )}{2 x + 7}

What is the extreme f(x)=x^3-4x^2+5x-2 ?
The extreme f(x)=x^3-4x^2+5x-2 is Maximum(1,0),Minimum(5/3 ,-4/27)