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Popular Functions >

extreme y=x(x-1)^5

Solution

extreme

Solution

Minimum (\frac{1}{6}, - \frac{3125}{46656}), Saddle (1, 0)

Solution steps

f^{'} (x) = (x - 1)^{4} (6 x - 1)

Find intervals:

Decreasing

: - \infty < x < \frac{1}{6},

Increasing

: \frac{1}{6} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = \frac{1}{6}

into

x (x - 1)^{5} : - \frac{3125}{46656}

Minimum (\frac{1}{6}, - \frac{3125}{46656})

Plug

x = 1

into

x (x - 1)^{5} : 0

Saddle (1, 0)

Minimum (\frac{1}{6}, - \frac{3125}{46656}), Saddle (1, 0)

Graph

Popular Examples

extreme f(x)=x^3+6x^2-6

extreme f(x,y)=xy+x^2+y^2-x+y+17

extreme f(x)=2x^3-3x^2-12x+1,-4<= x<= 5

extreme f(x)=sqrt(3)x+2cos(x)

extreme f(t)= t/(t-4)

Frequently Asked Questions (FAQ)

What is the extreme y=x(x-1)^5 ?
The extreme y=x(x-1)^5 is Minimum(1/6 ,-3125/46656),Saddle(1,0)