What is the extreme f(x)=x^3-4500x^2+6*10^6x ?

The extreme f(x)=x^3-4500x^2+6*10^6x is Maximum(1000,2500000000),Minimum(2000,2000^3-6000000000)

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extreme f(x)=x^3-4500x^2+6*10^6x

extreme points

f (x) = x^{3} - 4500 x^{2} + 6 \cdot 1 0^{6} x

Maximum (1000, 2500000000), Minimum (2000, 200 0^{3} - 6000000000)

Solution steps

f^{'} (x) = 3 x^{2} - 9000 x + 6000000

Find intervals:

Increasing

: - \infty < x < 1000,

Decreasing

: 1000 < x < 2000,

Increasing

: 2000 < x < \infty

Plug

x = 1000

into

x^{3} - 4500 x^{2} + 6 \cdot 1 0^{6} x : 2500000000

Maximum (1000, 2500000000)

Plug

x = 2000

into

x^{3} - 4500 x^{2} + 6 \cdot 1 0^{6} x : 200 0^{3} - 6000000000

Minimum (2000, 200 0^{3} - 6000000000)

Maximum (1000, 2500000000), Minimum (2000, 200 0^{3} - 6000000000)

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

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

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

E (a, b) = \frac{a ( a + b ) ^{2} ( a - b )}{a ^{2} - b ^{2}}

f (x) = (x^{2} - \frac{7}{3} x + \frac{13}{9}) e^{3 x}

What is the extreme f(x)=x^3-4500x^2+6*10^6x ?
The extreme f(x)=x^3-4500x^2+6*10^6x is Maximum(1000,2500000000),Minimum(2000,2000^3-6000000000)