Question

The intevral in which the function f(x) = 5 + 36x – 3x² increases will be ______.

Options

• (– ∞, 6)

• (6, ∞)

• (– 6, 6)

• (0, – 6)

Answer 1

The intevral in which the function f(x) = 5 + 36x – 3x² increases will be (– ∞, 6).

Explanation:

f(x) = 5 + 36x – 3x²

Differentiate w.r. to ‘x’

f'(x) = 0 + 36 – 6x

For increasing function

f'(x) > 0

`\implies` 36 – 6x > 0

`\implies` 36 > 6x

`\implies` x < 6

i.e., x ∈ (– ∞, 6)

Hence f(x) increases in (– ∞, 6).