What is the extreme 4x^3-210x^2+3600x-200 ?

The extreme 4x^3-210x^2+3600x-200 is Maximum(15,20050),Minimum(20,19800)

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extreme 4x^3-210x^2+3600x-200

extreme points

4 x^{3} - 210 x^{2} + 3600 x - 200

Maximum (15, 20050), Minimum (20, 19800)

Solution steps

f^{'} (x) = 12 x^{2} - 420 x + 3600

Find intervals:

Increasing

: - \infty < x < 15,

Decreasing

: 15 < x < 20,

Increasing

: 20 < x < \infty

Plug

x = 15

into

4 x^{3} - 210 x^{2} + 3600 x - 200 : 20050

Maximum (15, 20050)

Plug

x = 20

into

4 x^{3} - 210 x^{2} + 3600 x - 200 : 19800

Minimum (20, 19800)

Maximum (15, 20050), Minimum (20, 19800)

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

\frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 2 x

f (x) = 12 x - x^{3} - y (y^{2} + 3 y - 9) + 4

f (x) = - x - x^{2} (1 + 2)

f (x) = 64 - x^{2}

What is the extreme 4x^3-210x^2+3600x-200 ?
The extreme 4x^3-210x^2+3600x-200 is Maximum(15,20050),Minimum(20,19800)