Let `f` be a twice differentiable function such that `f^(prime prime)(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 (x) be twice differentiable function such that f'' (x) lt 0 in [0,2]. Then :

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

Let f be a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx and f(0) = (4-e^(2))/(3) . Find f(x) .

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

Let y=f(x) be a differentiable function such that f(−1)=2,f(2)=−1 and f(5)=3 If the equation f (x)=2f(x) has real root. Then find f(x)

Let f: (-1,1) rarr R be a differentiable function with f(0) = -1 and f'(0) = 1 let g(x) =[f(2f(x)+2)]^2 , then g'(0) =

Let f:R to R and h:R to R be differentiable functions such that f(x)=x^(3)+3x+2,g(f(x))=x and h(g(x))=x for all x in R . Then, h'(1) equals.

Let f(x) and g(x) be differentiable functions such that f(x)+ int_(0)^(x) g(t)dt= sin x(cos x- sin x) and (f'(x))^(2)+ (g(x))^(2) = 1,"then" f(x) and g (x) respectively , can be

For a twice differentiable function f(x),g(x) is defined as g(x)=f^(prime)(x)^2+f^(prime)(x)f(x)on[a , e]dot If for a

Let f : R ->(0,oo) and g : R -> R be twice differentiable functions such that f" and g" are continuous functions on R. suppose f^(prime)(2)=g(2)=0,f^"(2)!=0 and g'(2)!=0 , If lim_(x->2) (f(x)g(x))/(f'(x)g'(x))=1 then