What is the critical x^2(x+1)^3(x-4)^2 ?

The critical x^2(x+1)^3(x-4)^2 is x=-1,x=(2(4-sqrt(30)))/7 ,x=0,x=(2(4+sqrt(30)))/7 ,x=4

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critical x^2(x+1)^3(x-4)^2

critical points

x^{2} (x + 1)^{3} (x - 4)^{2}

x = - 1, x = \frac{2 ( 4 - 30 )}{7}, x = 0, x = \frac{2 ( 4 + 30 )}{7}, x = 4

Solution steps

x^{2} (x + 1)^{3} (x - 4)^{2}

Find where

f^{'} (x)

is equal to zero or undefined

x = - 1, x = \frac{2 ( 4 - 30 )}{7}, x = 0, x = \frac{2 ( 4 + 30 )}{7}, x = 4

Identify critical points not in

f (x)

domain

Domain of

x^{2} (x + 1)^{3} (x - 4)^{2} : - \infty < x < \infty

All critical points are in domain

x = - 1, x = \frac{2 ( 4 - 30 )}{7}, x = 0, x = \frac{2 ( 4 + 30 )}{7}, x = 4

y = 0

x^{2} + 8

x - 9

f (x) = \frac{1}{4} x - \frac{1}{10}

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

What is the critical x^2(x+1)^3(x-4)^2 ?
The critical x^2(x+1)^3(x-4)^2 is x=-1,x=(2(4-sqrt(30)))/7 ,x=0,x=(2(4+sqrt(30)))/7 ,x=4