The sum of the abosolute maximum and minimum values of the function f x = x 2 - 5 x + 6 - 3 x + 2 in the interval - 1 , 3 is equal to :

Step-by-step solution

Given, f x = x 2 - 5 x + 6 - 3 x + 2 ⇒ f x = x - 3 x - 2 - 3 x + 2 ⇒ f x = x 2 - 8 x + 8 ; x ∈ - 1 , 2 - x 2 + 2 x - 4 ; x ∈ ( 2 , 3 ] ⇒ f ' x = 2 x - 8 ; x ∈ - 1 , 2 - x + 2 ; x ∈ 2 , 3 Now point of extrema will be 2 x - 8 = 0 ⇒ x = 4 which is not in domain and - x + 2 = 0 ⇒ x = 2 Now for finding the value of global minima and maxima we will check the value of function at extrema points and boundary points, So, f x = x 2 - 8 x + 8 will give,   f - 1 =