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Popular >

extreme 2/5 x^5-14x^3+15

Solution

extreme points

\frac{2}{5} x^{5} - 14 x^{3} + 15

Solution

Maximum (- 21, - \frac{882 21}{5} + 29421 + 15), Saddle (0, 15), Minimum (21, \frac{882 21}{5} - 29421 + 15)

Solution steps

f^{'} (x) = 2 x^{4} - 42 x^{2}

Find intervals:

Increasing

: - \infty < x < - 21,

Decreasing

: - 21 < x < 0,

Decreasing

: 0 < x < 21,

Increasing

: 21 < x < \infty

Plug

x = - 21

into

\frac{2}{5} x^{5} - 14 x^{3} + 15 : - \frac{882 21}{5} + 29421 + 15

Maximum (- 21, - \frac{882 21}{5} + 29421 + 15)

Plug

x = 0

into

\frac{2}{5} x^{5} - 14 x^{3} + 15 : 15

Saddle (0, 15)

Plug

x = 21

into

\frac{2}{5} x^{5} - 14 x^{3} + 15 : \frac{882 21}{5} - 29421 + 15

Minimum (21, \frac{882 21}{5} - 29421 + 15)

Maximum (- 21, - \frac{882 21}{5} + 29421 + 15), Saddle (0, 15), Minimum (21, \frac{882 21}{5} - 29421 + 15)

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Frequently Asked Questions (FAQ)

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