What is the extreme y=x^3-2x^2-4x+1 ?

The extreme y=x^3-2x^2-4x+1 is Maximum(-2/3 , 67/27),Minimum(2,-7)

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extreme y=x^3-2x^2-4x+1

extreme points

y = x^{3} - 2 x^{2} - 4 x + 1

Maximum (- \frac{2}{3}, \frac{67}{27}), Minimum (2, - 7)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3},

Decreasing

: - \frac{2}{3} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - \frac{2}{3}

into

x^{3} - 2 x^{2} - 4 x + 1 : \frac{67}{27}

Maximum (- \frac{2}{3}, \frac{67}{27})

Plug

x = 2

into

x^{3} - 2 x^{2} - 4 x + 1 : - 7

Minimum (2, - 7)

Maximum (- \frac{2}{3}, \frac{67}{27}), Minimum (2, - 7)

f (x) = x^{4} - 50 x^{2}

\frac{6 x ^{2} + 1}{2 x ^{2} + x - 1}

f (x) = 5 t^{\frac{2}{3}} + t^{\frac{5}{3}}

y = 3 x^{5} - x^{3} + 5

7 x - 4 = 0

What is the extreme y=x^3-2x^2-4x+1 ?
The extreme y=x^3-2x^2-4x+1 is Maximum(-2/3 , 67/27),Minimum(2,-7)