Let `g(x)=2f(x/2)+f(2-x)a n df^('')(x)<0AAx in (0,2)dot` Then `g(x)` increases in (a)`(1/2,2)` (b) `(4/3,2)` (c)`(0,2)` (d) `(0,4/3)`

Let g(x)=2f(x/2)+f(2-x) and f''(x)<0 , AA x in (0,2) .Then g(x) increasing in

Let g(x)=2f((x)/(2))+f(1-x) and f'(x)<0 in 0<=x<=1 then g(x)

g(x)=2f((x)/(2))+f(2-x) and f'(x)<0AA x in(0,2) If g(x) increases in (a,b) and decreases in (c,d), then the value of a+b+c+d-(2)/(3) is

Let g(x) = 2 f(x/2)+ f(2-x) and f''(x) lt 0 forall x in (0,2) . Then calculate the interval in which g(x) is increasing.

Let g(x)=f(tanx)+f(cotx),AAx in ((pi)/(2),pi). If f''(x)lt0,AAx in ((pi)/(2),pi), then

Let f''(x) gt 0 AA x in R and g(x)=f(2-x)+f(4+x). Then g(x) is increasing in

Let g^(prime)(x)>0a n df^(prime)(x)<0AAx in Rdot Then (f(x+1))>g(f(x-1)) f(g(x-1))>f(g(x+1)) g(f(x+1))

If f"(x)>0AAx in R ,f'(3)=0,a n dg(x)=f("tan"hat2x-2"tan"x+4),0

Let f(x)=e^(x)g(x),g(0)=4 and g'(0)=2, then f'(0) equals

Consider the function f(x) and g(x) such that f(x)=(x^(2))/(2)+1-x+int g(x)dx Range of the function f(x) is [0,(2)/(e^(2))] (b) [0,(4)/(e^(2))][0,(4)/(e)] (d) (0,e^(2))