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Popular >

extreme 13x(x-1)^3

Solution

extreme points

13 x (x - 1)^{3}

Solution

Minimum (\frac{1}{4}, - \frac{351}{256}), Saddle (1, 0)

Solution steps

f^{'} (x) = 13 ((x - 1)^{3} + 3 x (x - 1)^{2})

Find intervals:

Decreasing

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

Increasing

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

Increasing

: 1 < x < \infty

Plug

x = \frac{1}{4}

into

13 x (x - 1)^{3} : - \frac{351}{256}

Minimum (\frac{1}{4}, - \frac{351}{256})

Plug

x = 1

into

13 x (x - 1)^{3} : 0

Saddle (1, 0)

Minimum (\frac{1}{4}, - \frac{351}{256}), Saddle (1, 0)

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

Frequently Asked Questions (FAQ)

What is the extreme 13x(x-1)^3 ?
The extreme 13x(x-1)^3 is Minimum(1/4 ,-351/256),Saddle(1,0)