On which two intervals is the function increasing
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On which two intervals is the function increasing

[From: ] [author: ] [Date: 12-04-01] [Hit: ]
Where does this function achieve its minimum?f(x) = x^6(x + 8)(9x + 56)....Did my work on paper,......
The function f(x)=(x^7)(x+8)^2 is defined on the interval [-10,14]
On which two intervals is the function increasing?
Find the region where the function is positive.
Where does this function achieve its minimum?

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f(x) = (x^7)(x + 8)²

f'(x) = x^6(x + 8)(9x + 56)....Did my work on paper, too lazy to show it :P

Set f'(x) = 0 to find the max/min of the function and test these values for increase and decrease.

0 = x^6(x + 8)(9x + 56)
x = -8, - 56/9, 0

f' (-9) = +
f' (-7) = -
f' (-1) = +
f' (1) = +

The increasing intervals are [-10, -8) (-56/9, 0) (0, 14]

f(x) = (x^7)(x + 8)²
0 = (x^7)(x + 8)²
x = 0, -8

f (-9) = -
f (-1) = -
f (1) = +

The region where the function is positive is (0, 14]

f (-8) = 0
f (-56/9) = -1 141 231.024
f (0) = 0

The minimum must be (-6.2222, -1 141 231.024)
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