What is the extreme f(x)=-1000x^3-1000x^2+8000x+1000 ?

The extreme f(x)=-1000x^3-1000x^2+8000x+1000 is Minimum(-2,-11000),Maximum(4/3 , 203000/27)

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extreme f(x)=-1000x^3-1000x^2+8000x+1000

extreme points

f (x) = - 1000 x^{3} - 1000 x^{2} + 8000 x + 1000

Minimum (- 2, - 11000), Maximum (\frac{4}{3}, \frac{203000}{27})

Solution steps

f^{'} (x) = - 3000 x^{2} - 2000 x + 8000

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < \frac{4}{3},

Decreasing

: \frac{4}{3} < x < \infty

Plug

x = - 2

into

- 1000 x^{3} - 1000 x^{2} + 8000 x + 1000 : - 11000

Minimum (- 2, - 11000)

Plug

x = \frac{4}{3}

into

- 1000 x^{3} - 1000 x^{2} + 8000 x + 1000 : \frac{203000}{27}

Maximum (\frac{4}{3}, \frac{203000}{27})

Minimum (- 2, - 11000), Maximum (\frac{4}{3}, \frac{203000}{27})

\frac{1}{x} + ln (x)

f (x) = x^{3} - 3 x y + y^{3}

f (x, y) = y^{2} e^{- x + l n (y)}

f (x, y) = 49 - x^{2} - y^{2}

f (x) = \frac{1}{2} x^{4} - 3 x y + 3 y^{4}

What is the extreme f(x)=-1000x^3-1000x^2+8000x+1000 ?
The extreme f(x)=-1000x^3-1000x^2+8000x+1000 is Minimum(-2,-11000),Maximum(4/3 , 203000/27)