**HERE IS YOUR ANSWER**

**CORRECT QUESTION**

**Find the intervals in which the function f given by f(x) = 2x^2 − 3x is (a) strictly increasing (b) strictly decreasing**

**SOLUTION**

**Given, f(x) = 2x² - 3x
**

differentiate f(x) with respect to x,

f'(x) = 4x - 3 ------(1)

(a) when f(x) is strictly increasing function :

f'(x) > 0

from equation (1),

4x - 3 > 0 => x > 3/4

e.g., x ∈ (3/4, ∞ )

Therefore, the given function (f) is strictly increasing in interval x ∈ (3/4, ∞ ) .

(b) when f(x) is strictly decreasing function :

f'(x) < 0

from equation (1),

4x -3 < 0 => x < 3/4

e.g., x ∈ (-∞ , 3/4)

Therefore, the given function (f) is strictly decreasing in interval x ∈ (-∞ , 3/4)