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

Question

Philoid · Accepted Answer

(a) It is given that function f(x) = 2x² – 3x

⇒ f’(x) = 4x – 3

If f’(x) = 0, then we get,

So, the points divides the real line into two disjoint intervals, and

So, in interval, f’(x) = 4x -3 >0

Therefore, the given function (f) is strictly increasing in interval.

(b) It is given that function f(x) = 2x² – 3x

⇒ f’(x) = 4x – 3

If f’(x) = 0, then we get,

So, the points divides the real line into two disjoint intervals, and

So, in interval f’(x) = 4x -3 < 0

Therefore, the given function (f) is strictly decreasing in interval.