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

The extreme f(x)=-x^3-3x^4 is Maximum(-1/4 , 1/256),Saddle(0,0)

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

extreme points

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

Maximum (- \frac{1}{4}, \frac{1}{256}), Saddle (0, 0)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

: - \frac{1}{4} < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - \frac{1}{4}

into

- x^{3} - 3 x^{4} : \frac{1}{256}

Maximum (- \frac{1}{4}, \frac{1}{256})

Plug

x = 0

into

- x^{3} - 3 x^{4} : 0

Saddle (0, 0)

Maximum (- \frac{1}{4}, \frac{1}{256}), Saddle (0, 0)

2 x + y = 12

f (x) = \frac{( x + 1 )}{x ^{2} - 9}

f (x) = 4 + 4 + x

f (x) = - (4 x + 10 y) = - 9

f (x) = \frac{( 3 x - 8 )}{( x ^{2} - 9 x + 20 )}

What is the extreme f(x)=-x^3-3x^4 ?
The extreme f(x)=-x^3-3x^4 is Maximum(-1/4 , 1/256),Saddle(0,0)