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

The extreme f(x)=-x^4+3x^3+18 is Saddle(0,18),Maximum(9/4 , 6795/256)

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

extreme points

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

Saddle (0, 18), Maximum (\frac{9}{4}, \frac{6795}{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} + 18 : 18

Saddle (0, 18)

Plug

x = \frac{9}{4}

into

- x^{4} + 3 x^{3} + 18 : \frac{6795}{256}

Maximum (\frac{9}{4}, \frac{6795}{256})

Saddle (0, 18), Maximum (\frac{9}{4}, \frac{6795}{256})

f (x, y) = ln (y + x)

f (x, y) = x e^{y} + y + 1

f (x) = sin (x) - cos (x), 0 \leq x \leq π

f (x) = \frac{x}{e ^{x}}

f (x) = 3 (x - 5)^{2} + 1

What is the extreme f(x)=-x^4+3x^3+18 ?
The extreme f(x)=-x^4+3x^3+18 is Saddle(0,18),Maximum(9/4 , 6795/256)