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Popular Functions >

extreme f(x)=2x^36x^2-18x+1

Solution

extreme

Solution

Maximum (- 4 \frac{3}{10}, - 12 (\frac{3}{10})^{\frac{3}{4}} \frac{3}{10} + 18 4 \frac{3}{10} + 1), Minimum (4 \frac{3}{10}, 12 (\frac{3}{10})^{\frac{3}{4}} \frac{3}{10} - 18 4 \frac{3}{10} + 1)

Solution steps

f^{'} (x) = 60 x^{4} - 18

Find intervals:

Increasing

: - \infty < x < - 4 \frac{3}{10},

Decreasing

: - 4 \frac{3}{10} < x < 4 \frac{3}{10},

Increasing

: 4 \frac{3}{10} < x < \infty

Plug

x = - 4 \frac{3}{10}

into

2 x^{3} 6 x^{2} - 18 x + 1 : - 12 (\frac{3}{10})^{\frac{3}{4}} \frac{3}{10} + 18 4 \frac{3}{10} + 1

Maximum (- 4 \frac{3}{10}, - 12 (\frac{3}{10})^{\frac{3}{4}} \frac{3}{10} + 18 4 \frac{3}{10} + 1)

Plug

x = 4 \frac{3}{10}

into

2 x^{3} 6 x^{2} - 18 x + 1 : 12 (\frac{3}{10})^{\frac{3}{4}} \frac{3}{10} - 18 4 \frac{3}{10} + 1

Minimum (4 \frac{3}{10}, 12 (\frac{3}{10})^{\frac{3}{4}} \frac{3}{10} - 18 4 \frac{3}{10} + 1)

Maximum (- 4 \frac{3}{10}, - 12 (\frac{3}{10})^{\frac{3}{4}} \frac{3}{10} + 18 4 \frac{3}{10} + 1), Minimum (4 \frac{3}{10}, 12 (\frac{3}{10})^{\frac{3}{4}} \frac{3}{10} - 18 4 \frac{3}{10} + 1)

Graph

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Frequently Asked Questions (FAQ)

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