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Popular >

extreme f(x)=60x^3-120x

Solution

extreme points

f (x) = 60 x^{3} - 120 x

Solution

Maximum (- \frac{2}{3}, - 60 (\frac{2}{3})^{\frac{3}{2}} + 406), Minimum (\frac{2}{3}, 60 (\frac{2}{3})^{\frac{3}{2}} - 406)

Solution steps

f^{'} (x) = 180 x^{2} - 120

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

60 x^{3} - 120 x : - 60 (\frac{2}{3})^{\frac{3}{2}} + 406

Maximum (- \frac{2}{3}, - 60 (\frac{2}{3})^{\frac{3}{2}} + 406)

Plug

x = \frac{2}{3}

into

60 x^{3} - 120 x : 60 (\frac{2}{3})^{\frac{3}{2}} - 406

Minimum (\frac{2}{3}, 60 (\frac{2}{3})^{\frac{3}{2}} - 406)

Maximum (- \frac{2}{3}, - 60 (\frac{2}{3})^{\frac{3}{2}} + 406), Minimum (\frac{2}{3}, 60 (\frac{2}{3})^{\frac{3}{2}} - 406)

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