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Popular >

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

Solution

extreme points

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

Solution

Maximum (0, 5), Minimum (\frac{9 - 17}{8}, \frac{107 - 51 17}{512} + 5), Maximum (\frac{9 + 17}{8}, \frac{107 + 51 17}{512} + 5)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{9 - 17}{8},

Increasing

: \frac{9 - 17}{8} < x < \frac{9 + 17}{8},

Decreasing

: \frac{9 + 17}{8} < x < \infty

Plug

x = 0

into

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

Maximum (0, 5)

Plug

x = \frac{9 - 17}{8}

into

5 - 2 x^{2} + 3 x^{3} - x^{4} : \frac{107 - 51 17}{512} + 5

Minimum (\frac{9 - 17}{8}, \frac{107 - 51 17}{512} + 5)

Plug

x = \frac{9 + 17}{8}

into

5 - 2 x^{2} + 3 x^{3} - x^{4} : \frac{107 + 51 17}{512} + 5

Maximum (\frac{9 + 17}{8}, \frac{107 + 51 17}{512} + 5)

Maximum (0, 5), Minimum (\frac{9 - 17}{8}, \frac{107 - 51 17}{512} + 5), Maximum (\frac{9 + 17}{8}, \frac{107 + 51 17}{512} + 5)

Popular Examples

extreme f(x,y)=2+sqrt(9-x^2-y^2)extreme points

f (x, y) = 2 + 9 - x^{2} - y^{2}

extreme f(x)=x^2-5x+6 extreme points

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

extreme f(x)=xsqrt(x+2)extreme points

f (x) = x x + 2

extreme f(x)=4xy-x^4-y^4 extreme points

f (x) = 4 x y - x^{4} - y^{4}

extreme f(x,y)=6-3x-2y extreme points

f (x, y) = 6 - 3 x - 2 y

Frequently Asked Questions (FAQ)

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