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Popular >

extreme x^3(x-1)^2(7x-4)

Solution

extreme points

x^{3} (x - 1)^{2} (7 x - 4)

Solution

Saddle (0, 0), Minimum (\frac{4 - 2}{7}, - \frac{368 2 - 44}{16807}), Maximum (\frac{4 + 2}{7}, \frac{368 2 + 44}{16807}), Minimum (1, 0)

Solution steps

f^{'} (x) = 6 x^{2} (x - 1) (7 x^{2} - 8 x + 2)

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{4 - 2}{7},

Increasing

: \frac{4 - 2}{7} < x < \frac{4 + 2}{7},

Decreasing

: \frac{4 + 2}{7} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

x^{3} (x - 1)^{2} (7 x - 4) : 0

Saddle (0, 0)

Plug

x = \frac{4 - 2}{7}

into

x^{3} (x - 1)^{2} (7 x - 4) : - \frac{368 2 - 44}{16807}

Minimum (\frac{4 - 2}{7}, - \frac{368 2 - 44}{16807})

Plug

x = \frac{4 + 2}{7}

into

x^{3} (x - 1)^{2} (7 x - 4) : \frac{368 2 + 44}{16807}

Maximum (\frac{4 + 2}{7}, \frac{368 2 + 44}{16807})

Plug

x = 1

into

x^{3} (x - 1)^{2} (7 x - 4) : 0

Minimum (1, 0)

Saddle (0, 0), Minimum (\frac{4 - 2}{7}, - \frac{368 2 - 44}{16807}), Maximum (\frac{4 + 2}{7}, \frac{368 2 + 44}{16807}), Minimum (1, 0)

Graph

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Frequently Asked Questions (FAQ)

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