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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).

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Solution


(d) k ∈ (−∞, 4)

fx=x2-kx+5f'x=2x-kGiven: f(x) is increasing on[2, 4]. f'x>02x-k>0k<2xx2, 4, maximum value of k is 4, k < 4. k-, 4

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