Question

Let f(x)=max{5x, 52-2x2 }, where x is any positive real number. Then the minimum possible value of f(x) is

Answer 1

Given x is positive real number. The minimum value of the maximum {5x,52-2x2} will occur when both the graphs intersect. i.e., when 5x = 52-2x2
2x2+5x-52 = 0
2x2+13x-8x-52 = 0
x(2x+13)-4(2x+13) = 0
(x-4)(2x+13) = 0
x = 4 or -13/2
When x = 4, f(x) = 20