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Popular >

extreme f(x)=x^3-5x+2

Solution

extreme points

f (x) = x^{3} - 5 x + 2

Solution

Maximum (- \frac{5}{3}, - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3} + 2), Minimum (\frac{5}{3}, (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3} + 2)

Solution steps

f^{'} (x) = 3 x^{2} - 5

Find intervals:

Increasing

: - \infty < x < - \frac{5}{3},

Decreasing

: - \frac{5}{3} < x < \frac{5}{3},

Increasing

: \frac{5}{3} < x < \infty

Plug

x = - \frac{5}{3}

into

x^{3} - 5 x + 2 : - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3} + 2

Maximum (- \frac{5}{3}, - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3} + 2)

Plug

x = \frac{5}{3}

into

x^{3} - 5 x + 2 : (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3} + 2

Minimum (\frac{5}{3}, (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3} + 2)

Maximum (- \frac{5}{3}, - (\frac{5}{3})^{\frac{3}{2}} + 5 \frac{5}{3} + 2), Minimum (\frac{5}{3}, (\frac{5}{3})^{\frac{3}{2}} - 5 \frac{5}{3} + 2)

Graph

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Frequently Asked Questions (FAQ)

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