The range of the function f x = 3 - x + 2 + x is

Step-by-step solution

Given, f x = 3 - x + 2 + x Now differentiation the above function, f ' ( x ) = - 1 2 3 - x + 1 2 2 + x Point of maxima and minima, f ' ( x ) = 0 ⇒ 3 - x - 2 + x 2 2 + x 3 - x = 0 ⇒ 2 + x = 3 - x ⇒ x = 1 2 And domain is ( - 2 ≤ x ≤ 3 ) So at x = 1 2 , maxima The maximum value of the function, f 1 2 = 5 2 + 5 2 = 10 The minimum value of function at x = - 2   or   x = 3 f - 2 = 5 and f 3 = 5 Therefore, the range of the function, Range ∈ 5 , 10