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Popular >

extreme x^3-5x

Solution

extreme points

x^{3} - 5 x

Solution

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

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

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

Plug

x = \frac{5}{3}

into

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

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

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

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f (x) = 7 - 3 x

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\frac{10}{36 - x ^{2}}

Frequently Asked Questions (FAQ)

What is the extreme x^3-5x ?
The extreme x^3-5x is