Find the interval in which the function f(x) = 2x2 - 3x is strictly increasing ?

Question

Question

(\(\rm\frac{3}{4}\), ∞)
[\(\rm\frac{-3}{4}\), ∞)
(-∞ ,\(\rm\frac{3}{4}\)]
[\(\rm\frac{3}{4}\), 1)

duplicate options found. English Question 1 options 1,2

Answer 1

Concept:

If f′(x) > 0 at each point in an interval, then the function is said to be strictly increasing.

Calculations:

Given , f(x) = 2x2 - 3x

Differentiating, we get

f'(x) = 4x - 3

f(x) is strictly increasing function

∴ f'(x) > 0

⇒ 4x - 3 > 0

⇒ 4x > 3

⇒ x > \(\rm\frac{3}{4}\)

∴ x ∈ (\(\rm\frac{3}{4}\), ∞)

Important Points