Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.

Question

Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (Enter your answers using interval notation. If the answer cannot be expressed as an interval, enter EMPTY or ∅.)

f(x) = 5x² + 2x + 1

increasing
decreasing

Answer 1

We need to take the derivative, which is:

f'(x) = 10x + 2

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

f(x) increasing: (-1/5, ∞)

f(x) decreasing: (-∞, -1/5)