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Popular >

extreme f(x)=7x-x^3

Solution

extreme points

f (x) = 7 x - x^{3}

Solution

Minimum (- \frac{7}{3}, - 7 \frac{7}{3} + (\frac{7}{3})^{\frac{3}{2}}), Maximum (\frac{7}{3}, 7 \frac{7}{3} - (\frac{7}{3})^{\frac{3}{2}})

Solution steps

f^{'} (x) = 7 - 3 x^{2}

Find intervals:

Decreasing

: - \infty < x < - \frac{7}{3},

Increasing

: - \frac{7}{3} < x < \frac{7}{3},

Decreasing

: \frac{7}{3} < x < \infty

Plug

x = - \frac{7}{3}

into

7 x - x^{3} : - 7 \frac{7}{3} + (\frac{7}{3})^{\frac{3}{2}}

Minimum (- \frac{7}{3}, - 7 \frac{7}{3} + (\frac{7}{3})^{\frac{3}{2}})

Plug

x = \frac{7}{3}

into

7 x - x^{3} : 7 \frac{7}{3} - (\frac{7}{3})^{\frac{3}{2}}

Maximum (\frac{7}{3}, 7 \frac{7}{3} - (\frac{7}{3})^{\frac{3}{2}})

Minimum (- \frac{7}{3}, - 7 \frac{7}{3} + (\frac{7}{3})^{\frac{3}{2}}), Maximum (\frac{7}{3}, 7 \frac{7}{3} - (\frac{7}{3})^{\frac{3}{2}})

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f (x) = - x^{3} + 3 x - 4

extreme f(x)=-x^3+3x-9 extreme points

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=7x-x^3 ?
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