Question

If f(x) = x⁵ – 20x³ + 240x, then f(x) satisfies ______.

Options

• It is monotonically decreasing everywhere

• It is monotonically decreasing on (0, ∞)

• It is monotonically increasing on (–∞, 0)

• It is monotonically increasing everywhere

Answer 1

If f(x) = x⁵ – 20x³ + 240x, then f(x) satisfies it is monotonically increasing everywhere.

Explanation:

f(x) = x⁵ – 20x³ + 240x

Differentiating the above function w.r.t.x, we get

f′(x) = 5x⁴ – 60x² + 240

= 5(x⁴ – 12x² + 48) > 0 for x∈R

So, f(x) is increasing for x∈R.