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?
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)
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)