Question

The function f(x)=x^3+6x^2+8x

Answer 1

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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