JEE Main 2024 Mathematics question
Let f(x) = 2ˣ – x², x ∈ ℝ. If m and n are respectively the number of points at which the curves y = f(x) and y = f ′(x) intersect the x-axis then the value of m + n is
Answer: 5
Solution
f(x) = 0 means 2ˣ = x², which has 3 solutions (one negative root and x = 2, x = 4), so m = 3. f′(x) = 2ˣ ln 2
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