JEE Main 2024 Mathematics question
For the function f(x) = (cos x) − x + 1, x ∈ R, between the following two statements (S1) f(x) = 0 for only one value of x in [0, π]. (S2) f(x) is decreasing in and increasing in
Answer: (B)
Solution
f′(x) = −sin x − 1 ≤ 0, so f is decreasing on all of [0, π] (S2 is false). f(0) = 2 and f(π) = −π
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