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Popular Functions >

extreme-4x^4+3x^3+3x^2

Solution

extreme points

- 4 x^{4} + 3 x^{3} + 3 x^{2}

Solution

Maximum (\frac{9 - 465}{32}, \frac{9 ( 4019 - 155 465 )}{32768}), Minimum (0, 0), Maximum (\frac{9 + 465}{32}, \frac{9 ( 4019 + 155 465 )}{32768})

Solution steps

f^{'} (x) = - 16 x^{3} + 9 x^{2} + 6 x

Find intervals:

Increasing

: - \infty < x < \frac{9 - 465}{32},

Decreasing

: \frac{9 - 465}{32} < x < 0,

Increasing

: 0 < x < \frac{9 + 465}{32},

Decreasing

: \frac{9 + 465}{32} < x < \infty

Plug

x = \frac{9 - 465}{32}

into

- 4 x^{4} + 3 x^{3} + 3 x^{2} : \frac{9 ( 4019 - 155 465 )}{32768}

Maximum (\frac{9 - 465}{32}, \frac{9 ( 4019 - 155 465 )}{32768})

Plug

x = 0

into

- 4 x^{4} + 3 x^{3} + 3 x^{2} : 0

Minimum (0, 0)

Plug

x = \frac{9 + 465}{32}

into

- 4 x^{4} + 3 x^{3} + 3 x^{2} : \frac{9 ( 4019 + 155 465 )}{32768}

Maximum (\frac{9 + 465}{32}, \frac{9 ( 4019 + 155 465 )}{32768})

Maximum (\frac{9 - 465}{32}, \frac{9 ( 4019 - 155 465 )}{32768}), Minimum (0, 0), Maximum (\frac{9 + 465}{32}, \frac{9 ( 4019 + 155 465 )}{32768})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme-4x^4+3x^3+3x^2 ?
The extreme-4x^4+3x^3+3x^2 is