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Popular >

extreme f(x)=2x^5+10x^4+x^3-10

Solution

extreme points

f (x) = 2 x^{5} + 10 x^{4} + x^{3} - 10

Solution

Maximum (- \frac{20 + 370}{10}, \frac{56225 + 2923 370}{250} - 10), Minimum (\frac{- 20 + 370}{10}, \frac{56225 - 2923 370}{250} - 10), Saddle (0, - 10)

Solution steps

f^{'} (x) = 10 x^{4} + 40 x^{3} + 3 x^{2}

Find intervals:

Increasing

: - \infty < x < - \frac{20 + 370}{10},

Decreasing

: - \frac{20 + 370}{10} < x < \frac{370 - 20}{10},

Increasing

: \frac{370 - 20}{10} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{20 + 370}{10}

into

2 x^{5} + 10 x^{4} + x^{3} - 10 : \frac{56225 + 2923 370}{250} - 10

Maximum (- \frac{20 + 370}{10}, \frac{56225 + 2923 370}{250} - 10)

Plug

x = \frac{- 20 + 370}{10}

into

2 x^{5} + 10 x^{4} + x^{3} - 10 : \frac{56225 - 2923 370}{250} - 10

Minimum (\frac{- 20 + 370}{10}, \frac{56225 - 2923 370}{250} - 10)

Plug

x = 0

into

2 x^{5} + 10 x^{4} + x^{3} - 10 : - 10

Saddle (0, - 10)

Maximum (- \frac{20 + 370}{10}, \frac{56225 + 2923 370}{250} - 10), Minimum (\frac{- 20 + 370}{10}, \frac{56225 - 2923 370}{250} - 10), Saddle (0, - 10)

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=2x^5+10x^4+x^3-10 ?
The extreme f(x)=2x^5+10x^4+x^3-10 is