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)=`

Let f be a twice differentiable function such that f''(x)=-f(x), and f'(x)=g(x),h(x)=[f(x)]^(2)+[g(x)]^(2) Find h(10) if h(5)=11

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

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(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

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

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)), then h'(1) is equal to

Let f be a twice differentiable function such that f''(x)gt 0 AA x in R . Let h(x) is defined by h(x)=f(sin^(2)x)+f(cos^(2)x) where |x|lt (pi)/(2) . The number of critical points of h(x) are