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Popular Functions >

extreme 3x(x-3)^3

Solution

extreme

Solution

Minimum (\frac{3}{4}, - \frac{6561}{256}), Saddle (3, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < \frac{3}{4},

Increasing

: \frac{3}{4} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = \frac{3}{4}

into

3 x (x - 3)^{3} : - \frac{6561}{256}

Minimum (\frac{3}{4}, - \frac{6561}{256})

Plug

x = 3

into

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

Saddle (3, 0)

Minimum (\frac{3}{4}, - \frac{6561}{256}), Saddle (3, 0)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme 3x(x-3)^3 ?
The extreme 3x(x-3)^3 is Minimum(3/4 ,-6561/256),Saddle(3,0)