Question

If the function f(x) = x² – kx + 5 is increasing on [2, 4], then

A. k ∈ (2, ∞)

B. k ∈ (–∞, 2)

C. k ∈ (4, ∞)

D. k ∈ (–∞, 4)

Answer 1

Correct answer is D.

Formula:-

(i) The necessary and sufficient condition for differentiable function defined on (a, b) to be strictly increasing on (a, b) is that f’(x) > 0 for all x ∈ (a, b)

Given:-

For increasing function f’(x) > 0

2x - k > 0

\(\Rightarrow\) K < 2x

Putting x = 2

K < 4

\(\Rightarrow\) k ∈ (–∞, 4)