If f(x) is a differentiable function for all x R such that f(x) has fundamental period 2, f(x)=0 has exactly two solution in [0,2] . also f(0) 0 . If minimum number of e r o s of h(x)=f(x) x-f(x) x in [0.99) is 120+ k then k is

Step-by-step solution

h(x)= d d x (f(x) x) first find the minimum number of zeroes of (f(x) x)=0f(x)=0 has minimum 98 roots in 0,99) cosx =0 has 31 roots in [0,99) maximum common possible root is only I hence minimum number of roots of f(x) x=0 is 128 . Hence d d x (f(x) x)=0 has minimum 127 roots.