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Popular Functions >

extreme f(x)=9x^5-2x^4-2x^3+4

Solution

extreme points

f (x) = 9 x^{5} - 2 x^{4} - 2 x^{3} + 4

Solution

Maximum (\frac{4 - 286}{45}, \frac{69784 286 - 848296}{20503125} + 4), Saddle (0, 4), Minimum (\frac{4 + 286}{45}, \frac{- 848296 - 69784 286}{20503125} + 4)

Solution steps

f^{'} (x) = 45 x^{4} - 8 x^{3} - 6 x^{2}

Find intervals:

Increasing

: - \infty < x < \frac{4 - 286}{45},

Decreasing

: \frac{4 - 286}{45} < x < 0,

Decreasing

: 0 < x < \frac{4 + 286}{45},

Increasing

: \frac{4 + 286}{45} < x < \infty

Plug

x = \frac{4 - 286}{45}

into

9 x^{5} - 2 x^{4} - 2 x^{3} + 4 : \frac{69784 286 - 848296}{20503125} + 4

Maximum (\frac{4 - 286}{45}, \frac{69784 286 - 848296}{20503125} + 4)

Plug

x = 0

into

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

Saddle (0, 4)

Plug

x = \frac{4 + 286}{45}

into

9 x^{5} - 2 x^{4} - 2 x^{3} + 4 : \frac{- 848296 - 69784 286}{20503125} + 4

Minimum (\frac{4 + 286}{45}, \frac{- 848296 - 69784 286}{20503125} + 4)

Maximum (\frac{4 - 286}{45}, \frac{69784 286 - 848296}{20503125} + 4), Saddle (0, 4), Minimum (\frac{4 + 286}{45}, \frac{- 848296 - 69784 286}{20503125} + 4)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=9x^5-2x^4-2x^3+4 ?
The extreme f(x)=9x^5-2x^4-2x^3+4 is