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Popular Functions >

extreme f(x)=(x^2-4)^4(x^2+1)^5

Solution

extreme

Solution

Minimum (- 2, 0), Maximum (- \frac{4}{3}, \frac{5 ^{14} \cdot 256}{387420489}), Minimum (0, 256), Maximum (\frac{4}{3}, \frac{5 ^{14} \cdot 256}{387420489}), Minimum (2, 0)

Solution steps

f^{'} (x) = 2 x (x + 2)^{3} (x - 2)^{3} (3 x + 4) (3 x - 4) (x^{2} + 1)^{4}

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < - \frac{4}{3},

Decreasing

: - \frac{4}{3} < x < 0,

Increasing

: 0 < x < \frac{4}{3},

Decreasing

: \frac{4}{3} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

(x^{2} - 4)^{4} (x^{2} + 1)^{5} : 0

Minimum (- 2, 0)

Plug

x = - \frac{4}{3}

into

(x^{2} - 4)^{4} (x^{2} + 1)^{5} : \frac{5 ^{14} \cdot 256}{387420489}

Maximum (- \frac{4}{3}, \frac{5 ^{14} \cdot 256}{387420489})

Plug

x = 0

into

(x^{2} - 4)^{4} (x^{2} + 1)^{5} : 256

Minimum (0, 256)

Plug

x = \frac{4}{3}

into

(x^{2} - 4)^{4} (x^{2} + 1)^{5} : \frac{5 ^{14} \cdot 256}{387420489}

Maximum (\frac{4}{3}, \frac{5 ^{14} \cdot 256}{387420489})

Plug

x = 2

into

(x^{2} - 4)^{4} (x^{2} + 1)^{5} : 0

Minimum (2, 0)

Minimum (- 2, 0), Maximum (- \frac{4}{3}, \frac{5 ^{14} \cdot 256}{387420489}), Minimum (0, 256), Maximum (\frac{4}{3}, \frac{5 ^{14} \cdot 256}{387420489}), Minimum (2, 0)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x^2-4)^4(x^2+1)^5 ?
The extreme f(x)=(x^2-4)^4(x^2+1)^5 is