What is the extreme f(x)=x^3+4x^2+5x-2 ?

The extreme f(x)=x^3+4x^2+5x-2 is Maximum(-5/3 ,-104/27),Minimum(-1,-4)

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extreme f(x)=x^3+4x^2+5x-2

extreme points

f (x) = x^{3} + 4 x^{2} + 5 x - 2

Maximum (- \frac{5}{3}, - \frac{104}{27}), Minimum (- 1, - 4)

Solution steps

f^{'} (x) = 3 x^{2} + 8 x + 5

Find intervals:

Increasing

: - \infty < x < - \frac{5}{3},

Decreasing

: - \frac{5}{3} < x < - 1,

Increasing

: - 1 < x < \infty

Plug

x = - \frac{5}{3}

into

x^{3} + 4 x^{2} + 5 x - 2 : - \frac{104}{27}

Maximum (- \frac{5}{3}, - \frac{104}{27})

Plug

x = - 1

into

x^{3} + 4 x^{2} + 5 x - 2 : - 4

Minimum (- 1, - 4)

Maximum (- \frac{5}{3}, - \frac{104}{27}), Minimum (- 1, - 4)

3 x^{2} y + y^{3} - 3 x^{2} - 3 y^{2} + 2

f (x, y) = 4 x^{2} + 4 y^{2} - 4 x - 8 y

f (x, y) = 10 x y - 5 x^{2} - 7 y^{2} + 40 x

f (x) = ln (1 + 8 x^{3})

f (x, y) = x^{4} + y^{4} - 4 x y

What is the extreme f(x)=x^3+4x^2+5x-2 ?
The extreme f(x)=x^3+4x^2+5x-2 is Maximum(-5/3 ,-104/27),Minimum(-1,-4)