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Popular >

extreme f(x)=x^4-7x^3-11x^2

Solution

extreme points

f (x) = x^{4} - 7 x^{3} - 11 x^{2}

Solution

Minimum (\frac{21 - 793}{8}, \frac{5551 793 - 157931}{512}), Maximum (0, 0), Minimum (\frac{21 + 793}{8}, - \frac{157931 + 5551 793}{512})

Solution steps

f^{'} (x) = 4 x^{3} - 21 x^{2} - 22 x

Find intervals:

Decreasing

: - \infty < x < \frac{21 - 793}{8},

Increasing

: \frac{21 - 793}{8} < x < 0,

Decreasing

: 0 < x < \frac{21 + 793}{8},

Increasing

: \frac{21 + 793}{8} < x < \infty

Plug

x = \frac{21 - 793}{8}

into

x^{4} - 7 x^{3} - 11 x^{2} : \frac{5551 793 - 157931}{512}

Minimum (\frac{21 - 793}{8}, \frac{5551 793 - 157931}{512})

Plug

x = 0

into

x^{4} - 7 x^{3} - 11 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{21 + 793}{8}

into

x^{4} - 7 x^{3} - 11 x^{2} : - \frac{157931 + 5551 793}{512}

Minimum (\frac{21 + 793}{8}, - \frac{157931 + 5551 793}{512})

Minimum (\frac{21 - 793}{8}, \frac{5551 793 - 157931}{512}), Maximum (0, 0), Minimum (\frac{21 + 793}{8}, - \frac{157931 + 5551 793}{512})

Popular Examples

asymptotes of (2x)/(x-3)asymptotes

\frac{2 x}{x - 3}

extreme f(x)= 3/(x-5)extreme points

f (x) = \frac{3}{x - 5}

range of f(x)=-x^2+4 range

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

inverse of f(x)=ln(x-3)+7 inverse

f (x) = ln (x - 3) + 7

inverse of f(x)=-(0.009(x-220)^2-220)inverse

f (x) = - (0.009 (x - 220)^{2} - 220)

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