If `f"(x)>0AAx in R ,f'(3)=0,a n df(x)=f("tan"hat2x-2"tan"x+4),0

If f''(x) gt forall in R, f(3)=0 and g(x) =f(tan^(2)x-2tanx+4y)0ltxlt(pi)/(2) ,then g(x) is increasing in

Let f: R->R 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

If f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dxdot

If f(x)=|x a a a x a a a x|=0, then f^(prime)(x)=0a n df^(x)=0 has common root f^(x)=0a n df^(prime)(x)=0 has common root sum of roots of f(x)=0 is -3a none of these

If f(x) satisfies the relation f((5x-3y)/2)=(5f(x)-3f(y))/2AAx ,y in R , and f(0)=3a n df^(prime)(0)=2, then the period of "sin"(f(x)) is (a) 2pi (b) pi (c) 3pi (d) 4pi

f:[0,5]rarrR,y=f(x) such that f''(x)=f''(5-x)AAx in [0,5] f'(0)=1 and f'(5)=7 , then the value of int_(1)^(4)f'(x)dx is

If a function 'f' satisfies the relation f(x)f^('')(x)-f(x)f^(')(x) -f^(')(x)^(2)=0 AA x in R and f(0)=1=f^(')(0) . Then find f(x) .

A function f: RvecR satisfies the equation f(x+y)=f(x)f(y) for all x , y in Ra n df(x)!=0fora l lx in Rdot If f(x) is differentiable at x=0a n df^(prime)(0)=2, then prove that f^(prime)(x)=2f(x)dot

Check the nature of the following differentiable functions (i) f(x) = e^(x) +sin x ,x in R^(+) (ii) f(x)=sinx+tan x- 2x,x in(0,pi//2)

If f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1, then find the value of f(7)dot