CAT 2018 Slot 2 — QA Question 31
Basics (Functions)Easy
Let f(x) = max {5x, 52 – 2x2}, where x is any positive real number. Then the minimum possible value of f(x) is
Answer & solution
Answer: 20
Solution
The graph of the function 52 – 2x2 will be of ‘inverted U’ shape, while the graph of the function y = 5x will be a straight line with a positive slope.
Therefore, the minimum value of the required function will be obtained at a point of intersection of y = 52 – 2x2 and y = 5x.
Therefore, 52 – 2x2 = 5x or 2x2 + 5x – 52 = 0.
∴ (x - 4)(2x + 13) = 0
∴ x = 4 or x =
Since x is a positive real number, x = 4.
At x = 4, 5x = 52 – 2x2 = 20
Hence, 20.