If `f` is a real function such that `f(x)>0,f^(prime)(xx)` is continuous for all real `xa n da xf^(prime)(x)geq2sqrt(f(x))-2af(x),(a x!=2),` show that `sqrt(f(x))geq(sqrt(f(1)))/x ,xgeq1.`

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) for all x ,

Find f'(x) if f(x)=sqrt(x^(2)+1)

Find f'(x) if f(x)=sqrt(x^(2)+1)

Find f'(x) if f(x)=sqrt(x^(2)-1)

Let g^(prime)(x)>0a n df^(prime)(x) g(f(x-1)) f(g(x+1))>f(g(x-1)) g(f(x+1))

f(x)=sqrt(x^(2)+1) then lim_(xto3)(f(x)-sqrt(10))/(x-3) is

Let f: RvecR be a function satisfying condition f(x+y^3)=f(x)+[f(y)]^3 for all x ,y in Rdot If f^(prime)(0)geq0, find f(10)dot

Let f be a function such that f(x+y)=f(x)+f(y) for all xa n dya n df(x)=(2x^2+3x)g(x) for all x , where g(x) is continuous and g(0)=3. Then find f^(prime)(x)dot

"If " (d)/(dx)f(x)=f'(x), " then " int(xf'(x)-2f(x))/(sqrt(x^(4)f(x)))dx is equal to

Let f(x)a n dg(x) be differentiable functions such that f^(prime)(x)g(x)!=f(x)g^(prime)(x) for any real xdot Show that between any two real solution of f(x)=0, there is at least one real solution of g(x)=0.