Home
Class 12
MATHS
If f: RvecRa n dg: RvecR are two functio...

If `f: RvecRa n dg: RvecR` are two functions such that `f(x)+f^(x)=-xg(x)f^(prime)(x)a n dg(x)>0AAx in Rdot` Then the function `f^2(x)+f('(x))^2` has a maxima at `x=0` a minima at `x=0` a point of inflexion at `x=0` none of these

Promotional Banner

Similar Questions

Explore conceptually related problems

If f''(x)>0 and Q(x)=2f((x^2)/2)+f(6-x^2),AAx in R , then function Q(x) is

A cubic polynomial function f(x) has a local maxima at x=1 and local minima at x=0 .If f(1)=3 and f(0)=0, then f(2) is

If f and g are continuous functions on [0,a] such that f(x)=f(a-x) and g(x)+g(a-x)=2 then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx

If f: RvecR is a differentiable function such that f^(prime)(x)>2f(x)fora l lxRa n df(0)=1,t h e n : f(x) is decreasing in (0,oo) f^(prime)(x) e^(2x)in(0,oo)

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) .

Let f(x) be a function such that,f(0)=f'(0)=0,f''(x)=sec^(4)x+4 then the function is