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

Step-by-step solution

aligned & f(x)= ₀^ x^2 t^2-8 t+15 e^t d t, x R & f^ (x)= x^4-8 x^2+15 e^ x^2 (2 x)=0 & 2 (x^2-5 ) (x^2-3 ) e^ x^2 =0 & x(x+ 5 )(x- 5 )(x+ 3 )(x- 3 )=0 aligned By using wavy curve method Number of local maximum =2 Number of local minimum =3