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find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (enter your answers using interval notation. if an answer does not exist, enter dne.)



Answer :

We need to take the derivative, which is:

[tex]f'(x) = 10x + 2[/tex]

and see where it is positive (increasing) and negative (decreasing). We see that [tex]f'(x) = 0 at x = -1/5, f'(x) < 0 for x < -1/5, and f'(x) > 0 for x > -1/5[/tex]. Therefore, we have

f(x) increasing: (-1/5, ∞)

f(x) decreasing: (-∞, -1/5)

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