Let `f: RvecR` be a continuous onto function satisfying `f(x)+f(-x)=0AAx in Rdot` If `f(-3)=2a n df(5)=4in[-5,5],` then the minimum number of roots of the equation `f(x)=0` is

Let f:R rarr R be a continuous onto function satisfying f(x)+f(-x)=0AA x in R, If f(-3)=2 and f(5)=4 in [-5,5], then the equation f(x)=0 has

Let f be a differentiable function satisfying f '(x) =2 f(x) +10 AA x in R and f (0) =0, then the number of real roots of the equation f (x)+ 5 sec ^(2) x=0 ln (0, 2pi) is:

Let f be a continuous function satisfying f'(In x)=[1 for 0 1 and f(0)=0 then f(x) can be defined as

Let f(x) be a continuous & differentiable function on R satisfying f(-x)=f(x)&f(3+x)=f(3-x)AA x in R . If f'(1)=-5 then f'(7) =

Let f(x) is a continuous function such that f(-1) = -2,f(0) = -1,f(1) = 0,f (2) = 1, f(3) = 0,f (4) = -1 and f(5) = 1 then minimum number of roots of f'(x) + xf " (x) = 0 in the interval (-1,5) are

There exists a function f(x) satisfying 'f (0)=1,f(0)=-1,f(x) lt 0,AAx and

A function y=f(x) satisfying f'(x)=x^(-(3)/(2)),f'(4)=2 and f(0)=0 is