What is the extreme 1/3 x^3-9x^2+72x+2 ?

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

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extreme 1/3 x^3-9x^2+72x+2

extreme points

\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) = \frac{e ^{x^{2} + x + 2}}{x}

x 9 - x

f (x) = 2 x^{3} - 6 x^{2} - 18 x + 54

f (x) = \frac{1}{4} e^{x} + e^{- x}

f (x) = \frac{5 x}{x ^{2} + 16}, 0 \leq x \leq 12

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