Let f x = x - 1 x 2 - 2 x - 3 + x - 3 , x ∈ ℝ . If m and M are respectively the number of points of local minimum and local maximum of f in the interval 0 , 4 , then m + M is equal to _____.

Question

Let f x = x - 1 x 2 - 2 x - 3 + x - 3 , x &#8712; &#8477; . If m and M are respectively the number of points of local minimum and local maximum of f in the interval 0 , 4 , then m + M is equal to _____.

Quantrex Academy · Accepted Answer

Correct answer: 0

Given, f x = x - 1 x + 1 x - 3 + x - 3 f x = x - 3 x 2 , 3 &#8804; x &#8804; 4 x - 3 2 - x 2 , 1 &#8804; x &#60; 3 x - 3 x 2 , 0 &#60; x &#60; 1 f ' x = 3 x 2 - 6 x , 3 &#60; x &#60; 4 - 3 x 2 + 6 x + 2 , 1 &#60; x &#60; 3 3 x 2 - 6 x , 0 &#60; x &#60; 1 f ' 3 + &#62; 0 f ' 3 - &#60; 0 &#8594; Minimum f ' 1 + &#62; 0 f ' 1 - &#60; 0 &#8594; Minimum For x &#8712; 1 , 3 , f ' x = 0 at one point &#8594; Maximum For x &#8712; 3 , 4 , &#160; f ' x &#8800; 0 For x &#8712; 0 , 1 , &#160; f &#39

Let f x = x - 1 x 2 - 2 x - 3 + x - 3 , x ∈ ℝ . If m and M are respectively the number of points of local minimum and local maximum of f in the interval 0 , 4 , then m + M is equal to _____.

Correct answer

Step-by-step solution

More from Application of Derivatives

Let f x = x - 1 x 2 - 2 x - 3 + x - 3 , x &#8712; &#8477; . If m and M are respectively the number of points of local minimum and local maximum of f in the interval 0 , 4 , then m + M is equal to _____.

Correct answer

Step-by-step solution

More from Application of Derivatives

Let f x = x - 1 x 2 - 2 x - 3 + x - 3 , x ∈ ℝ . If m and M are respectively the number of points of local minimum and local maximum of f in the interval 0 , 4 , then m + M is equal to _____.