JEE Advanced2021MathematicsApplication of DerivativesActual
Let f₁:(0, ) R and f₂:(0, ) R be defined by f₁(x)= ₀^ x _ j=1 ²¹(t-j)^ j d t, x > 0 and f₂(x)=98(x-1)⁵⁰-600(x-1)⁴⁹+2450, x > 0 where, for any positive integer n and real numbers a₁, a₂, , a_ n , _ i=1 ^ n a_ i denotes the product of a₁, a₂, , a_ n . Let m_ i and n_ i , respectively, denote the number of points of local minima and the number of points of local maxima of function f_ i , i=1,2 , in the interval (0, ) .
Correct answer
0
Step-by-step solution
f 2 x = 98 x - 1 50 - 600 x - 1 49 + 2450 ,    x > 0 f 2 ' x = 98 × 50 x − 1 49 − 600 × 49 x − 1 48 = 4900 x − 1 48 x − 1 − 6 = 4900 x − 1 48 x − 7 So extrema is at x = 7 only, which is minima m 2 = 1 , n 2 = 0 Hence 6 m 2 + 4 n 2 + 8 m 2 n 2 = 6