Function of the form max {f(x) g(x) h(x) }

Let f (x), g(x) be two real valued functions then the function h(x) =2 max {f(x)-g(x), 0} is equal to :

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(x) = ||x| -1| , g(x) = |x| + |x-2| , h (x) = max, { 1,x,x^(3)} If a, b,c are the no .of points where f(x), g(x) and h(x) , are not differentiable then the value of a+ b + c is …..\

Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

The function f(x) = max. {(1-x), (1+x), 2}, x in (-oo, oo) is

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

Suppose f, g, and h be three real valued function defined on R. Let f(x) = 2x + |x|, g(x) = (1)/(3)(2x-|x|) and h(x) = f(g(x)) The domain of definition of the function l (x) = sin^(-1) ( f(x) - g (x) ) is equal to

If f_r(x),g_r(x),h_r(x),r=1,2,3 are differentiable function and y=|(f_1(x), g_1(x), h_1(x)), (f_2(x), g_2(x), h_2(x)),(f_3(x), g_3(x), h_3(x))| then dy/dx= |(f\'_1(x), g\'_1(x), h\'_1(x)), (f_2(x), g_2(x), h_2(x)),(f_3(x), g_3(x), h_3(x))|+ |(f_1(x), g_1(x), h_1(x)), (f\'_2(x), g\'_2(x), h\'_2(x)),(f_3(x), g_3(x), h_3(x))|+|(f_1(x), g_1(x), h_1(x)), (f_2(x), g_2(x), h_2(x)),(f\'_3(x), g\'_3(x), h\'_3(x))| On the basis of above information, answer the following question: Let f(x)=|(x^4, cosx, sinx),(24, 0, 1),(a, a^2, a^3)| , where a is a constant Then at x= pi/2, d^4/dx^4{f(x)} is (A) 0 (B) a (C) a+a^3 (D) a+a^4