What is the extreme f(x)=x^3+8x^2+16x+25 ?

The extreme f(x)=x^3+8x^2+16x+25 is Maximum(-4,25),Minimum(-4/3 , 419/27)

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extreme f(x)=x^3+8x^2+16x+25

extreme points

f (x) = x^{3} + 8 x^{2} + 16 x + 25

Maximum (- 4, 25), Minimum (- \frac{4}{3}, \frac{419}{27})

Solution steps

f^{'} (x) = 3 x^{2} + 16 x + 16

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

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

Increasing

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

Plug

x = - 4

into

x^{3} + 8 x^{2} + 16 x + 25 : 25

Maximum (- 4, 25)

Plug

x = - \frac{4}{3}

into

x^{3} + 8 x^{2} + 16 x + 25 : \frac{419}{27}

Minimum (- \frac{4}{3}, \frac{419}{27})

Maximum (- 4, 25), Minimum (- \frac{4}{3}, \frac{419}{27})

4 x + 5 y = - 10

- ln (x + 3)

f (x) = 3 x - 5

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

y = 2 x - 1

What is the extreme f(x)=x^3+8x^2+16x+25 ?
The extreme f(x)=x^3+8x^2+16x+25 is Maximum(-4,25),Minimum(-4/3 , 419/27)