JEE Main 2024 Mathematics question
Consider the function f : [1/2, 1] → ℝ defined by f(x) = 4√2x³ – 3√2x – 1. Consider the statements (I) The curve y = f(x) intersects the x-axis exactly at one point. (II) The curve y = f(x) intersects the x-axis at x = cos(π/12). Then
Answer: (D)
Solution
f′(x) = 12√2x² − 3√2 > 0 on [1/2, 1], f(1/2) < 0 and f(1) > 0, so there is exactly one zero in the interval: (I) is correct. With x = cos
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