What is the extreme f(x)=x^3-5x^2+7x-3 ?

The extreme f(x)=x^3-5x^2+7x-3 is Maximum(1,0),Minimum(7/3 ,-32/27)

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extreme f(x)=x^3-5x^2+7x-3

extreme points

f (x) = x^{3} - 5 x^{2} + 7 x - 3

Maximum (1, 0), Minimum (\frac{7}{3}, - \frac{32}{27})

Solution steps

f^{'} (x) = 3 x^{2} - 10 x + 7

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < \frac{7}{3},

Increasing

: \frac{7}{3} < x < \infty

Plug

x = 1

into

x^{3} - 5 x^{2} + 7 x - 3 : 0

Maximum (1, 0)

Plug

x = \frac{7}{3}

into

x^{3} - 5 x^{2} + 7 x - 3 : - \frac{32}{27}

Minimum (\frac{7}{3}, - \frac{32}{27})

Maximum (1, 0), Minimum (\frac{7}{3}, - \frac{32}{27})

f (x) = 3 x^{2} - 4 y^{3} - 6 x + 48 y - 1

f (x) = x^{2} + y^{2} - 8 x + y

f (x) = 12 x^{3} - 9 x^{2} - 108 x + 4

f (x) = 3 x^{2} + 6 x - 6

f (x) = 3 x - 3

What is the extreme f(x)=x^3-5x^2+7x-3 ?
The extreme f(x)=x^3-5x^2+7x-3 is Maximum(1,0),Minimum(7/3 ,-32/27)