What is the extreme f(x)=x^3+9x^2+b ?

The extreme f(x)=x^3+9x^2+b is Maximum(-6,b+108),Minimum(0,b)

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extreme f(x)=x^3+9x^2+b

extreme points

f (x) = x^{3} + 9 x^{2} + b

Maximum (- 6, b + 108), Minimum (0, b)

Solution steps

f^{'} (x) = 3 x^{2} + 18 x

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 6

into

x^{3} + 9 x^{2} + b : b + 108

Maximum (- 6, b + 108)

Plug

x = 0

into

x^{3} + 9 x^{2} + b : b

Minimum (0, b)

Maximum (- 6, b + 108), Minimum (0, b)

e^{x - y} (y^{2} - 2 x^{2})

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

\frac{d}{d x} (x y^{2})

f (x) = x^{3} - x^{2} - x - 10

y = 2 x^{3} + 3 x^{2} - 36 x + 4

What is the extreme f(x)=x^3+9x^2+b ?
The extreme f(x)=x^3+9x^2+b is Maximum(-6,b+108),Minimum(0,b)