What is the extreme f(x)= 1/3 x^3-9x^2+72x+2 ?

The extreme f(x)= 1/3 x^3-9x^2+72x+2 is Maximum(6,182),Minimum(12,146)

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extreme f(x)= 1/3 x^3-9x^2+72x+2

extreme points

f (x) = \frac{1}{3} x^{3} - 9 x^{2} + 72 x + 2

Maximum (6, 182), Minimum (12, 146)

Solution steps

f^{'} (x) = x^{2} - 18 x + 72

Find intervals:

Increasing

: - \infty < x < 6,

Decreasing

: 6 < x < 12,

Increasing

: 12 < x < \infty

Plug

x = 6

into

\frac{1}{3} x^{3} - 9 x^{2} + 72 x + 2 : 182

Maximum (6, 182)

Plug

x = 12

into

\frac{1}{3} x^{3} - 9 x^{2} + 72 x + 2 : 146

Minimum (12, 146)

Maximum (6, 182), Minimum (12, 146)

F (x, y) = x^{3} y^{2} + x^{2} y + 2 x y^{2} + 2 y

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

f (x) = (\frac{x}{5})^{5} - (\frac{4 x}{4})^{4} + 5

f (x) = x^{\frac{1}{3}} - x^{- \frac{2}{3}}

f (x) = 2 x + 4 y

What is the extreme f(x)= 1/3 x^3-9x^2+72x+2 ?
The extreme f(x)= 1/3 x^3-9x^2+72x+2 is Maximum(6,182),Minimum(12,146)