If f(x) = `x/ (x + tanx)`, x belongs to (0, `pi`/2) (A) f(x) has exactly one point of maxima (C) f(x) is increasing in (0, `pi`/2) ) ( (B) f(x) has exactly one point of minima (D) none of these

f(x) = (x)/(1 + x tan x), x in (0, (pi)/(2)) then a)f(x) has exactly one point of minima b)f(x) has exactly one point of maxima c)f(x) is increasing in (0, (pi)/(2)) . d)f(x) is decreasing in (0, (pi)/(2)) .

Let f(x) =x^(2) , x in (-1,2) Then show that f(x) has exactly one point of local minima but global maximum Is not defined.

Let f (x) = x^(2) , x in [-1 , 2) Then show that f(x) has exactly one point of local minima but global maximum is not defined.

f(x) is cubic polynomial with f(x)=18 and f(1)=-1 . Also f(x) has local maxima at x=-1 and f^(prime)(x) has local minima at x=0 , then (A) the distance between (-1,2)a n d(af(a)), where x=a is the point of local minima is 2sqrt(5) (B) f(x) is increasing for x in [1,2sqrt(5]) (C) f(x) has local minima at x=1 (D)the value of f(0)=15

Find the points of local maxima or minima for f(x) =" sin "2x -x, x in (0,pi)

If f(x)=sgn(sin^(2)x-sin x-1) has exactly four points of discontinuity for x in(0,n pi),n in N, then

Let f(x)= 3/(x-2)+4/(x-3)+5/(x-4) . Then f(x)=0 has (A) exactly one real root in (2,3) (B) exactly one real root in (3,4) (C) at least one real root in (2,3) (D) none of these

Let f(x)= 3/(x-2)+4/(x-3)+5/(x-4) . Then f(x)=0 has (A) exactly one real root in (2,3) (B) exactly one real root in (3,4) (C) at least one real root in (2,3) (D) none of these