What is the extreme f(x)=x^{11}-9x^7+5x-3 ?

The extreme f(x)=x^{11}-9x^7+5x-3 is

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extreme f(x)=x^{11}-9x^7+5x-3

extreme points

f (x) = x^{11} - 9 x^{7} + 5 x - 3

Maximum (- \frac{5.96543 E 15}{2.5 E 15}, - (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} + 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} - 5 \frac{5.96543 E 15}{2.5 E 15} - 3), Minimum (- \frac{4.34574 E 15}{1.0 E 16}, - (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} + 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} - 5 \frac{4.34574 E 15}{1.0 E 16} - 3), Maximum (\frac{4.34574 E 15}{1.0 E 16}, (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} - 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} + 5 \frac{4.34574 E 15}{1.0 E 16} - 3), Minimum (\frac{5.96543 E 15}{2.5 E 15}, (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} - 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} + 5 \frac{5.96543 E 15}{2.5 E 15} - 3)

Solution steps

Find the critical points:

x = - \frac{5.96543 E 15}{2.5 E 15}, x = - \frac{4.34574 E 15}{1.0 E 16}, x = \frac{4.34574 E 15}{1.0 E 16}, x = \frac{5.96543 E 15}{2.5 E 15}

Domain of

x^{11} - 9 x^{7} + 5 x - 3 : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < - \frac{5.96543 E 15}{2.5 E 15},

Decreasing

: - \frac{5.96543 E 15}{2.5 E 15} < x < - \frac{4.34574 E 15}{1.0 E 16},

Increasing

: - \frac{4.34574 E 15}{1.0 E 16} < x < \frac{4.34574 E 15}{1.0 E 16},

Decreasing

: \frac{4.34574 E 15}{1.0 E 16} < x < \frac{5.96543 E 15}{2.5 E 15},

Increasing

: \frac{5.96543 E 15}{2.5 E 15} < x < \infty

Plug the extreme point

x = - \frac{5.96543 E 15}{2.5 E 15}

into

x^{11} - 9 x^{7} + 5 x - 3 \Rightarrow y = - (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} + 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} - 5 \frac{5.96543 E 15}{2.5 E 15} - 3

Maximum (- \frac{5.96543 E 15}{2.5 E 15}, - (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} + 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} - 5 \frac{5.96543 E 15}{2.5 E 15} - 3)

Plug the extreme point

x = - \frac{4.34574 E 15}{1.0 E 16}

into

x^{11} - 9 x^{7} + 5 x - 3 \Rightarrow y = - (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} + 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} - 5 \frac{4.34574 E 15}{1.0 E 16} - 3

Minimum (- \frac{4.34574 E 15}{1.0 E 16}, - (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} + 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} - 5 \frac{4.34574 E 15}{1.0 E 16} - 3)

Plug the extreme point

x = \frac{4.34574 E 15}{1.0 E 16}

into

x^{11} - 9 x^{7} + 5 x - 3 \Rightarrow y = (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} - 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} + 5 \frac{4.34574 E 15}{1.0 E 16} - 3

Maximum (\frac{4.34574 E 15}{1.0 E 16}, (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} - 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} + 5 \frac{4.34574 E 15}{1.0 E 16} - 3)

Plug the extreme point

x = \frac{5.96543 E 15}{2.5 E 15}

into

x^{11} - 9 x^{7} + 5 x - 3 \Rightarrow y = (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} - 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} + 5 \frac{5.96543 E 15}{2.5 E 15} - 3

Minimum (\frac{5.96543 E 15}{2.5 E 15}, (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} - 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} + 5 \frac{5.96543 E 15}{2.5 E 15} - 3)

Maximum (- \frac{5.96543 E 15}{2.5 E 15}, - (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} + 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} - 5 \frac{5.96543 E 15}{2.5 E 15} - 3), Minimum (- \frac{4.34574 E 15}{1.0 E 16}, - (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} + 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} - 5 \frac{4.34574 E 15}{1.0 E 16} - 3), Maximum (\frac{4.34574 E 15}{1.0 E 16}, (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} - 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} + 5 \frac{4.34574 E 15}{1.0 E 16} - 3), Minimum (\frac{5.96543 E 15}{2.5 E 15}, (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} - 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} + 5 \frac{5.96543 E 15}{2.5 E 15} - 3)

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

f (x) = 2 x^{2} + 3 x - 1

f (x) = ln (6 - ln (x))

7 x^{4} - 4 x^{2} - 8 x - 5

1 - (y + 1) 1 - y^{2} + y

What is the extreme f(x)=x^{11}-9x^7+5x-3 ?
The extreme f(x)=x^{11}-9x^7+5x-3 is