Let f ( x ) = ∫ 0 x 2 e t t 2 − 8 t + 15 dt , x ∈ R . Then the numbers of local maximum and local minimum points of f , respectively, are :

Question

Let f ( x ) = ∫ 0 x 2 ​ e t t 2 − 8 t + 15 ​ dt , x ∈ R . Then the numbers of local maximum and local minimum points of f , respectively, are :

TestHub · Accepted Answer

​ f ( x ) = ∫ 0 x 2 ​ e t t 2 − 8 t + 15 ​ d t , x ∈ R f ′ ( x ) = e x 2 x 4 − 8 x 2 + 15 ​ ( 2 x ) = 0 ⇒ e x 2 2 × ( x 2 − 5 ) ( x 2 − 3 ) ​ = 0 ⇒ x ( x + 5 ​ ) ( x − 5 ​ ) ( x + 3 ​ ) ( x − 3 ​ ) = 0 ​ By using wavy curve method Number of local maximum = 2 Number of local minimum = 3

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