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

The extreme f(x)=-x^4+3x^3-2 is Saddle(0,-2),Maximum(9/4 , 1675/256)

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

extreme points

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

Saddle (0, - 2), Maximum (\frac{9}{4}, \frac{1675}{256})

Solution steps

f^{'} (x) = - 4 x^{3} + 9 x^{2}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{9}{4},

Decreasing

: \frac{9}{4} < x < \infty

Plug

x = 0

into

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

Saddle (0, - 2)

Plug

x = \frac{9}{4}

into

- x^{4} + 3 x^{3} - 2 : \frac{1675}{256}

Maximum (\frac{9}{4}, \frac{1675}{256})

Saddle (0, - 2), Maximum (\frac{9}{4}, \frac{1675}{256})

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

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

\frac{x ^{2} - 3 x - 2}{x ^{2} - 4}

x - 3 - 3

f (x) = 64 - x^{2}

What is the extreme f(x)=-x^4+3x^3-2 ?
The extreme f(x)=-x^4+3x^3-2 is Saddle(0,-2),Maximum(9/4 , 1675/256)