What is the extreme f(x)=-(x+1)^2*(x+3)^3*(x-4)^2 ?

The extreme f(x)=-(x+1)^2*(x+3)^3*(x-4)^2 is

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extreme f(x)=-(x+1)^2(x+3)^3(x-4)^2

extreme

Saddle (- 3, 0), Minimum (\frac{3 - 849}{14}, - \frac{6356351448 - 262734936 849}{3294172} - 432), Maximum (- 1, 0), Minimum (\frac{3 + 849}{14}, - \frac{6356351448 + 262734936 849}{3294172} - 432), Maximum (4, 0)

Solution steps

f^{'} (x) = - 2 x (x + 3)^{3} (x - 4)^{2} - 2 (x + 3)^{3} (x - 4)^{2} - 5 x^{6} - 14 x^{5} + 74 x^{4} + 260 x^{3} + 51 x^{2} - 342 x - 216

Find intervals:

Decreasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < \frac{3 - 849}{14},

Increasing

: \frac{3 - 849}{14} < x < - 1,

Decreasing

: - 1 < x < \frac{3 + 849}{14},

Increasing

: \frac{3 + 849}{14} < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 3

into

- (x + 1)^{2} \cdot (x + 3)^{3} \cdot (x - 4)^{2} : 0

Saddle (- 3, 0)

Plug

x = \frac{3 - 849}{14}

into

- (x + 1)^{2} \cdot (x + 3)^{3} \cdot (x - 4)^{2} : - \frac{6356351448 - 262734936 849}{3294172} - 432

Minimum (\frac{3 - 849}{14}, - \frac{6356351448 - 262734936 849}{3294172} - 432)

Plug

x = - 1

into

- (x + 1)^{2} \cdot (x + 3)^{3} \cdot (x - 4)^{2} : 0

Maximum (- 1, 0)

Plug

x = \frac{3 + 849}{14}

into

- (x + 1)^{2} \cdot (x + 3)^{3} \cdot (x - 4)^{2} : - \frac{6356351448 + 262734936 849}{3294172} - 432

Minimum (\frac{3 + 849}{14}, - \frac{6356351448 + 262734936 849}{3294172} - 432)

Plug

x = 4

into

- (x + 1)^{2} \cdot (x + 3)^{3} \cdot (x - 4)^{2} : 0

Maximum (4, 0)

Saddle (- 3, 0), Minimum (\frac{3 - 849}{14}, - \frac{6356351448 - 262734936 849}{3294172} - 432), Maximum (- 1, 0), Minimum (\frac{3 + 849}{14}, - \frac{6356351448 + 262734936 849}{3294172} - 432), Maximum (4, 0)

What is the extreme f(x)=-(x+1)^2*(x+3)^3*(x-4)^2 ?
The extreme f(x)=-(x+1)^2*(x+3)^3*(x-4)^2 is