What is the extreme f(x)=x^3-5x^2+3x+1 ?

The extreme f(x)=x^3-5x^2+3x+1 is Maximum(1/3 , 40/27),Minimum(3,-8)

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extreme f(x)=x^3-5x^2+3x+1

extreme points

f (x) = x^{3} - 5 x^{2} + 3 x + 1

Maximum (\frac{1}{3}, \frac{40}{27}), Minimum (3, - 8)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < \frac{1}{3},

Decreasing

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

Increasing

: 3 < x < \infty

Plug

x = \frac{1}{3}

into

x^{3} - 5 x^{2} + 3 x + 1 : \frac{40}{27}

Maximum (\frac{1}{3}, \frac{40}{27})

Plug

x = 3

into

x^{3} - 5 x^{2} + 3 x + 1 : - 8

Minimum (3, - 8)

Maximum (\frac{1}{3}, \frac{40}{27}), Minimum (3, - 8)

g (x) = tan (x) + sec (x) - e x

y = x + 1

5 sin (x) + 5 cos (x)

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

f (x) = \frac{2}{3} x + 6

What is the extreme f(x)=x^3-5x^2+3x+1 ?
The extreme f(x)=x^3-5x^2+3x+1 is Maximum(1/3 , 40/27),Minimum(3,-8)