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Popular Functions >

extreme y=x^3-2x+4

Solution

extreme

Solution

Maximum (- \frac{2}{3}, - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} + 4), Minimum (\frac{2}{3}, (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} + 4)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3},

Decreasing

: - \frac{2}{3} < x < \frac{2}{3},

Increasing

: \frac{2}{3} < x < \infty

Plug

x = - \frac{2}{3}

into

x^{3} - 2 x + 4 : - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} + 4

Maximum (- \frac{2}{3}, - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} + 4)

Plug

x = \frac{2}{3}

into

x^{3} - 2 x + 4 : (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} + 4

Minimum (\frac{2}{3}, (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} + 4)

Maximum (- \frac{2}{3}, - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} + 4), Minimum (\frac{2}{3}, (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} + 4)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme y=x^3-2x+4 ?
The extreme y=x^3-2x+4 is