What is the extreme f(x)=6x^3+54x^2+144x+54 ?

The extreme f(x)=6x^3+54x^2+144x+54 is Maximum(-4,-42),Minimum(-2,-66)

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extreme f(x)=6x^3+54x^2+144x+54

extreme points

f (x) = 6 x^{3} + 54 x^{2} + 144 x + 54

Maximum (- 4, - 42), Minimum (- 2, - 66)

Solution steps

f^{'} (x) = 18 x^{2} + 108 x + 144

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < - 2,

Increasing

: - 2 < x < \infty

Plug

x = - 4

into

6 x^{3} + 54 x^{2} + 144 x + 54 : - 42

Maximum (- 4, - 42)

Plug

x = - 2

into

6 x^{3} + 54 x^{2} + 144 x + 54 : - 66

Minimum (- 2, - 66)

Maximum (- 4, - 42), Minimum (- 2, - 66)

(x - 7) (x^{2} - 14 x - 98)

y = (4 - x) \cdot 4^{x}

f (x) = 3 + 3 x - 3 x^{2}, 0 \leq x \leq 3

100

f (x) = \frac{1}{x ^{2} + 1}

What is the extreme f(x)=6x^3+54x^2+144x+54 ?
The extreme f(x)=6x^3+54x^2+144x+54 is Maximum(-4,-42),Minimum(-2,-66)