JEE Main 2025 Mathematics question
Let (2, 3) be the largest open interval in which the function f(x) = 2 (x - 2) - x + ax + 1 is strictly increasing and (b, c) be the largest open interval, in which the function g(x) = (x - 1)(x + 2 - a) is strictly decreasing. Then 100(a + b - c) is equal to :
Answer: (2)
Solution
a = 4 (minimum). g(x) = (x--, g'(x)<0 for x ∈ (8/5, 2). So b=8/5, c=2. 100(4+8/5-2) = 360.