Let `f` be a twice differentiable function such that `f^(x)=-f(x),a n df^(prime)(x)=g(x),h(x)=[f(x)]^2+[g(x)]^2dot` Find `h(10)ifh(5)=11`

Let f be a twice differentiable function such that f''(x)=-f(x)" and "f'(x)=g(x)."If "h'(x)=[f(x)]^(2)+[g(x)]^(2), h(a)=8" and "h(0)=2," then "h(2)=

STATEMENT - 1 : Let f be a twice differentiable function such that f'(x) = g(x) and f''(x) = - f (x) . If h'(x) = [f(x)]^(2) + [g (x)]^(2) , h(1) = 8 and h (0) =2 Rightarrow h(2) =14 and STATEMENT - 2 : h''(x)=0

If f(x) is a twice differentiable function such that f'' (x) =-f,f'(x)=g(x),h(x)=f^2(x)+g^2(x) and h(10)=10 , then h (5) is equal to

Let f be twice differentiable function such that g'(x)=-(f(x))/(g(x)),f'(x)=(g(x))/(f(x))h(x)=e^((f(x))^(2)+(g(x))^(2)+x)If h(5)=e^(6) then h(10) is equal to

If f is twice differentiable such that f"(x)=-f(x) f'(x)=g(x),h'(x)=[f(x)]^(2)+[g(x)]^(2)andh(0)=2, h(1)=4, then the equation y=h(x) represents.

Let f be a differentiable function such that f(0)=e^(2) and f'(x)=2f(x) for all x in R If h(x)=f(f(x)) ,then h'(0) is equal to

If f is twice differentiable such that f^(')(x)=-f(x) and f^(prime)(x)=g(x)dot If h(x) is twice differentiable function such that h^(prime)(x)=(f(x))^2+(g(x))^2dot If h(0)=2,h(1)=4, then the equation y=h(x) represents (a)a curve of degree 2 (b)a curve passing through the origin (c)a straight line with slope 2 (d)a straight line with y intercept equal to 2.

Let f be a differentiable function satisfying f(x/y)=f(x)-f(y) for all x ,\ y > 0. If f^(prime)(1)=1 then find f(x)dot