Question

Find the interval in which function f(x) = x^2 – 4x + 5 is decreasing.

(a) (2, ∞)

(b) (-∞, 2)

(c) (3, ∞)

(d) (-∞, ∞)

This question was posed to me in an interview for job.

My question is based upon Derivatives Application in section Application of Derivatives of Mathematics – Class 12

Answer 1

The correct choice is (b) (-∞, 2)

The best explanation: f(x) = x^2 – 4x + 5.

f’(x) = 2x – 4. Therefore f’(x) = 0 gives x = 2.

Now this point x=2 divides the line into two disjoint intervals and the interval namely (-∞, 2) is decreasing on f(x).