What is the extreme f(x)=3-16x+18x^2-2x^3-x^4 ?

The extreme f(x)=3-16x+18x^2-2x^3-x^4 is Maximum(-4,227),Minimum(1/2 ,-13/16),Maximum(2,11)

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extreme f(x)=3-16x+18x^2-2x^3-x^4

extreme points

f (x) = 3 - 16 x + 18 x^{2} - 2 x^{3} - x^{4}

Maximum (- 4, 227), Minimum (\frac{1}{2}, - \frac{13}{16}), Maximum (2, 11)

Solution steps

f^{'} (x) = - 4 x^{3} - 6 x^{2} + 36 x - 16

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < \frac{1}{2},

Increasing

: \frac{1}{2} < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 4

into

3 - 16 x + 18 x^{2} - 2 x^{3} - x^{4} : 227

Maximum (- 4, 227)

Plug

x = \frac{1}{2}

into

3 - 16 x + 18 x^{2} - 2 x^{3} - x^{4} : - \frac{13}{16}

Minimum (\frac{1}{2}, - \frac{13}{16})

Plug

x = 2

into

3 - 16 x + 18 x^{2} - 2 x^{3} - x^{4} : 11

Maximum (2, 11)

Maximum (- 4, 227), Minimum (\frac{1}{2}, - \frac{13}{16}), Maximum (2, 11)

f (x) = ∣ sin (x) ∣

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

x^{4} + 3 x y^{3} - x y

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

y = x^{2} + (z - 1)^{2}

What is the extreme f(x)=3-16x+18x^2-2x^3-x^4 ?
The extreme f(x)=3-16x+18x^2-2x^3-x^4 is Maximum(-4,227),Minimum(1/2 ,-13/16),Maximum(2,11)