If m and n respectively are the number of local maximum and local minimum points of the function f x = ∫ 0 x 2 t 2 - 5 t + 4 2 + e t d t , then the ordered pair m , n is equal to

Step-by-step solution

Given f x = ∫ 0 x 2 t 2 - 5 t + 4 2 + e t d t We know that, d d x ∫ u x v x f v d x = f v x d d x v u - f u x d d x u x Using above formula we get f ' x = x 4 - 5 x 2 + 4 2 + e x 2 · 2 x For critical points f ' x = 0 So, x x 2 - 1 x 2 - 4 2 + e x 2 = 0 ⇒ x x + 1 x - 1 x + 2 x - 2 = 0 Now by first derivative test we get, Here points of maxima are - 1 , 1 & points of minima are - 2 , 0 , 2