Question

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

(a) (2, ∞)

(b) (-∞, 2)

(c) (3, ∞)

(d) (-∞, ∞)

The question was asked during a job interview.

Enquiry is from Derivatives Application topic in portion Application of Derivatives of Mathematics – Class 12

Answer 1

Correct option is (a) (2, ∞)

To explain: 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 increasing on f(x).