What is the extreme f(x)=x^7(x+4)^4 ?

The extreme f(x)=x^7(x+4)^4 is Maximum(-4,0),Minimum(-28/11 ,-(2^{30}*823543)/(11^{11)}),Saddle(0,0)

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extreme f(x)=x^7(x+4)^4

extreme points

f (x) = x^{7} (x + 4)^{4}

Maximum (- 4, 0), Minimum (- \frac{28}{11}, - \frac{2 ^{30} \cdot 823543}{1 1 ^{11}}), Saddle (0, 0)

Solution steps

f^{'} (x) = x^{6} (x + 4)^{3} (11 x + 28)

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < - \frac{28}{11},

Increasing

: - \frac{28}{11} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 4

into

x^{7} (x + 4)^{4} : 0

Maximum (- 4, 0)

Plug

x = - \frac{28}{11}

into

x^{7} (x + 4)^{4} : - \frac{2 ^{30} \cdot 823543}{1 1 ^{11}}

Minimum (- \frac{28}{11}, - \frac{2 ^{30} \cdot 823543}{1 1 ^{11}})

Plug

x = 0

into

x^{7} (x + 4)^{4} : 0

Saddle (0, 0)

Maximum (- 4, 0), Minimum (- \frac{28}{11}, - \frac{2 ^{30} \cdot 823543}{1 1 ^{11}}), Saddle (0, 0)

f (x) = - x e^{- \frac{x}{2}}

x 36 - x

\frac{( x ^{2} - 8 )}{x - 3}

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

y = 21 x + 9 x^{2} - x^{3}

What is the extreme f(x)=x^7(x+4)^4 ?
The extreme f(x)=x^7(x+4)^4 is Maximum(-4,0),Minimum(-28/11 ,-(2^{30}*823543)/(11^{11)}),Saddle(0,0)