Q1. The function f (x) = a x , 0 < a < 1 is decreasing increasing strictly decreasing on R neither increasing or decreasing Solution f(x) = Let x 1 , x 2 ε R such that x 1 < x 2 . Then, x 1 < x 2 [ 0 < a < 1 & x 1 < x 2 ] f (x 1 ) > f (x 2 ) Thus, x 1 < x 2 => f (x 1 ) > f (x 2 ) for all x 1 , x 2 ε R Hence, f (x) is strictly decreasing function on R. Q2. Find two numbers whose sum is 24 and product is a large as possible. 10 and 14 20 and 4 ...