What is the extreme f(x)=-3x^4+8x^3-6x^2-2 ?

The extreme f(x)=-3x^4+8x^3-6x^2-2 is Maximum(0,-2),Saddle(1,-3)

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extreme f(x)=-3x^4+8x^3-6x^2-2

extreme points

f (x) = - 3 x^{4} + 8 x^{3} - 6 x^{2} - 2

Maximum (0, - 2), Saddle (1, - 3)

Solution steps

f^{'} (x) = - 12 x^{3} + 24 x^{2} - 12 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

- 3 x^{4} + 8 x^{3} - 6 x^{2} - 2 : - 2

Maximum (0, - 2)

Plug

x = 1

into

- 3 x^{4} + 8 x^{3} - 6 x^{2} - 2 : - 3

Saddle (1, - 3)

Maximum (0, - 2), Saddle (1, - 3)

f (x) = 14 x^{2} - 2 x^{3} + 2 y^{2} + 4 x y

\frac{4 x}{x ^{2} - 25}

f (x) = x^{2} + x y + y^{2} - 10 y + 33

f (x) = x^{3} - 6 x^{2} + 12 x + 1

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

What is the extreme f(x)=-3x^4+8x^3-6x^2-2 ?
The extreme f(x)=-3x^4+8x^3-6x^2-2 is Maximum(0,-2),Saddle(1,-3)