What is the extreme f(x)=-x^4+x^3+19 ?

The extreme f(x)=-x^4+x^3+19 is Saddle(0,19),Maximum(3/4 , 27/256+19)

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extreme f(x)=-x^4+x^3+19

extreme points

f (x) = - x^{4} + x^{3} + 19

Saddle (0, 19), Maximum (\frac{3}{4}, \frac{27}{256} + 19)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{3}{4},

Decreasing

: \frac{3}{4} < x < \infty

Plug

x = 0

into

- x^{4} + x^{3} + 19 : 19

Saddle (0, 19)

Plug

x = \frac{3}{4}

into

- x^{4} + x^{3} + 19 : \frac{27}{256} + 19

Maximum (\frac{3}{4}, \frac{27}{256} + 19)

Saddle (0, 19), Maximum (\frac{3}{4}, \frac{27}{256} + 19)

f (x) = \frac{x + 3}{x - 3}

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

f (x, y) = y e^{x^{2}}

f (x) = ln (y - x) + ln (y + x) + ln (16 - y)

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

What is the extreme f(x)=-x^4+x^3+19 ?
The extreme f(x)=-x^4+x^3+19 is Saddle(0,19),Maximum(3/4 , 27/256+19)