What is the extreme f(x)=x^3+10x^2+8 ?

The extreme f(x)=x^3+10x^2+8 is Maximum(-20/3 , 4216/27),Minimum(0,8)

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extreme f(x)=x^3+10x^2+8

extreme points

f (x) = x^{3} + 10 x^{2} + 8

Maximum (- \frac{20}{3}, \frac{4216}{27}), Minimum (0, 8)

Solution steps

f^{'} (x) = 3 x^{2} + 20 x

Find intervals:

Increasing

: - \infty < x < - \frac{20}{3},

Decreasing

: - \frac{20}{3} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{20}{3}

into

x^{3} + 10 x^{2} + 8 : \frac{4216}{27}

Maximum (- \frac{20}{3}, \frac{4216}{27})

Plug

x = 0

into

x^{3} + 10 x^{2} + 8 : 8

Minimum (0, 8)

Maximum (- \frac{20}{3}, \frac{4216}{27}), Minimum (0, 8)

f (x, y) = - 6 x^{2} + 5 x y - y^{2} + x + y

f (x, y) = (7 - x) (7 - y) (x + y - 7)

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

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

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

What is the extreme f(x)=x^3+10x^2+8 ?
The extreme f(x)=x^3+10x^2+8 is Maximum(-20/3 , 4216/27),Minimum(0,8)