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Popular >

extreme f(x)=x^4-7x^3-13x^2

Solution

extreme points

f (x) = x^{4} - 7 x^{3} - 13 x^{2}

Solution

Minimum (\frac{21 - 857}{8}, \frac{5999 857 - 178187}{512}), Maximum (0, 0), Minimum (\frac{21 + 857}{8}, - \frac{178187 + 5999 857}{512})

Solution steps

f^{'} (x) = 4 x^{3} - 21 x^{2} - 26 x

Find intervals:

Decreasing

: - \infty < x < \frac{21 - 857}{8},

Increasing

: \frac{21 - 857}{8} < x < 0,

Decreasing

: 0 < x < \frac{21 + 857}{8},

Increasing

: \frac{21 + 857}{8} < x < \infty

Plug

x = \frac{21 - 857}{8}

into

x^{4} - 7 x^{3} - 13 x^{2} : \frac{5999 857 - 178187}{512}

Minimum (\frac{21 - 857}{8}, \frac{5999 857 - 178187}{512})

Plug

x = 0

into

x^{4} - 7 x^{3} - 13 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{21 + 857}{8}

into

x^{4} - 7 x^{3} - 13 x^{2} : - \frac{178187 + 5999 857}{512}

Minimum (\frac{21 + 857}{8}, - \frac{178187 + 5999 857}{512})

Minimum (\frac{21 - 857}{8}, \frac{5999 857 - 178187}{512}), Maximum (0, 0), Minimum (\frac{21 + 857}{8}, - \frac{178187 + 5999 857}{512})

Popular Examples

global f(x)=-x^2+11 global extreme points

f (x) = - x^{2} + 11

inverse of f(x)=(x-8)^7 inverse

f (x) = (x - 8)^{7}

extreme f(x)=(4-3x)^2 extreme points

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

inflection f(x)=5x^3-3x inflection points

f (x) = 5 x^{3} - 3 x

domain of g(t)= 3/(sqrt(t))domain

g (t) = \frac{3}{t}

Frequently Asked Questions (FAQ)

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