What is the extreme f(x)=2x^3-x^2+16 ?

The extreme f(x)=2x^3-x^2+16 is Maximum(0,16),Minimum(1/3 , 431/27)

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extreme f(x)=2x^3-x^2+16

extreme points

f (x) = 2 x^{3} - x^{2} + 16

Maximum (0, 16), Minimum (\frac{1}{3}, \frac{431}{27})

Solution steps

f^{'} (x) = 6 x^{2} - 2 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \infty

Plug

x = 0

into

2 x^{3} - x^{2} + 16 : 16

Maximum (0, 16)

Plug

x = \frac{1}{3}

into

2 x^{3} - x^{2} + 16 : \frac{431}{27}

Minimum (\frac{1}{3}, \frac{431}{27})

Maximum (0, 16), Minimum (\frac{1}{3}, \frac{431}{27})

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

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

f (x) = x^{4} - 32 x + 4

f (x, y) = 12 x y - x^{2} - 3 y^{2}

f (x, y) = 4 x y^{2} - 2 x^{2} - 16 y^{2}

What is the extreme f(x)=2x^3-x^2+16 ?
The extreme f(x)=2x^3-x^2+16 is Maximum(0,16),Minimum(1/3 , 431/27)