The function increases in the interval (-∞, -3) and the function also increases in the interval (-1,∞) .
The given function is of the form
f(x) = x³ + 6x² + 8x
Now we take the first differentiation of the function
f'(x) = 2x² + 12x + 8
f'(x) = 2 (x² + 6x + 9) -10
f'(x) = 2(x+3)² - 10
Therefore at x = -3 , f'(x) = -10.
Hence the function is increasing in the interval of (-∞, -3)
Again f'(x) = 2x² + 12x + 8 , so after first differentiation we get :
That the function is also increasing in the interval (-1,∞)
Now for the interval (-4,-2), we can say that the graph of the function is positive as the y value increases and then decreases but all y values are positive as illustrated in the graph.
In the interval (0,∞) the function is strictly increasing and has positive values only.
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