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Popular >

extreme f(x)=x(x-5)^2(x+1)

Solution

extreme points

f (x) = x (x - 5)^{2} (x + 1)

Solution

Minimum (\frac{7 - 129}{8}, \frac{3 ( 4071 - 473 129 )}{512}), Maximum (\frac{7 + 129}{8}, \frac{3 ( 4071 + 473 129 )}{512}), Minimum (5, 0)

Solution steps

f^{'} (x) = (x - 5) (4 x^{2} - 7 x - 5)

Find intervals:

Decreasing

: - \infty < x < \frac{7 - 129}{8},

Increasing

: \frac{7 - 129}{8} < x < \frac{7 + 129}{8},

Decreasing

: \frac{7 + 129}{8} < x < 5,

Increasing

: 5 < x < \infty

Plug

x = \frac{7 - 129}{8}

into

x (x - 5)^{2} (x + 1) : \frac{3 ( 4071 - 473 129 )}{512}

Minimum (\frac{7 - 129}{8}, \frac{3 ( 4071 - 473 129 )}{512})

Plug

x = \frac{7 + 129}{8}

into

x (x - 5)^{2} (x + 1) : \frac{3 ( 4071 + 473 129 )}{512}

Maximum (\frac{7 + 129}{8}, \frac{3 ( 4071 + 473 129 )}{512})

Plug

x = 5

into

x (x - 5)^{2} (x + 1) : 0

Minimum (5, 0)

Minimum (\frac{7 - 129}{8}, \frac{3 ( 4071 - 473 129 )}{512}), Maximum (\frac{7 + 129}{8}, \frac{3 ( 4071 + 473 129 )}{512}), Minimum (5, 0)

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x(x-5)^2(x+1) ?
The extreme f(x)=x(x-5)^2(x+1) is