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Popular >

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

Solution

extreme points

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

Solution

Maximum (- \frac{6}{5}, - (\frac{6}{5})^{\frac{5}{2}} + 2 (\frac{6}{5})^{\frac{3}{2}} + 2), Saddle (0, 2), Minimum (\frac{6}{5}, (\frac{6}{5})^{\frac{5}{2}} - 2 (\frac{6}{5})^{\frac{3}{2}} + 2)

Solution steps

f^{'} (x) = 5 x^{4} - 6 x^{2}

Find intervals:

Increasing

: - \infty < x < - \frac{6}{5},

Decreasing

: - \frac{6}{5} < x < 0,

Decreasing

: 0 < x < \frac{6}{5},

Increasing

: \frac{6}{5} < x < \infty

Plug

x = - \frac{6}{5}

into

x^{5} - 2 x^{3} + 2 : - (\frac{6}{5})^{\frac{5}{2}} + 2 (\frac{6}{5})^{\frac{3}{2}} + 2

Maximum (- \frac{6}{5}, - (\frac{6}{5})^{\frac{5}{2}} + 2 (\frac{6}{5})^{\frac{3}{2}} + 2)

Plug

x = 0

into

x^{5} - 2 x^{3} + 2 : 2

Saddle (0, 2)

Plug

x = \frac{6}{5}

into

x^{5} - 2 x^{3} + 2 : (\frac{6}{5})^{\frac{5}{2}} - 2 (\frac{6}{5})^{\frac{3}{2}} + 2

Minimum (\frac{6}{5}, (\frac{6}{5})^{\frac{5}{2}} - 2 (\frac{6}{5})^{\frac{3}{2}} + 2)

Maximum (- \frac{6}{5}, - (\frac{6}{5})^{\frac{5}{2}} + 2 (\frac{6}{5})^{\frac{3}{2}} + 2), Saddle (0, 2), Minimum (\frac{6}{5}, (\frac{6}{5})^{\frac{5}{2}} - 2 (\frac{6}{5})^{\frac{3}{2}} + 2)

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^5-2x^3+2 ?
The extreme f(x)=x^5-2x^3+2 is