`f(x)=|a x-b|+c|x|AAx in (-oo,oo),` where `a >0, b >0,c > 0.` Find the condition if `f(x)` attains the minimum value only at one point.

Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x^2+a),a >0, which of the following is not true? maximum value of f is not attained even though f is bounded. f(x) is increasing on (0,oo) and has minimum at ,=0 f(x) is decreasing on (-oo,0) and has minimum at x=0. f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

Let f(x)=a+b|x|+c|x|^(4), where a,b, and c are real constants.Then,f(x) is differentiable at x=0, if a=0( b) b=0 (c) c=0( d) none of these

Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 AA x in (0,oo) also f (0)=0, Again f'(x) lt 0 AA x in (-oo, -1) and f '(x) gt AA x in (-1,oo) also f '(-1)=0 given lim _(x to oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. The minimum number of points where f'(x) is zero is:

If the range of the function f(x)=3x^(2)+bx+c is [0,oo) then value of (b^(2))/(3c) is

Let f(x)=a+b|x|+c|x|^(4), where a,b and c are real constants.Then,f(x) is differentiable at x=0, if a=0 (b) b=0( c) c=0(d) none of these

The value of b for which the function f(x)=sin x-bx+c is decreasing in the interval (-oo,oo) is given by

A function f(x) having the following properties, (i) f(x) is continuous except at x=3 (ii) f(x) is differentiable except at x=-2 and x=3 (iii) f(0) =0 lim_(x to 3) f(x) to - oo lim_(x to oo) f(x) =3 , lim_(x to oo) f(x)=0 (iv) f'(x) gt 0 AA in (-oo, -2) uu (3,oo) " and " f'(x) le 0 AA x in (-2,3) (v) f''(x) gt 0 AA x in (-oo,-2) uu (-2,0)" and "f''(x) lt 0 AA x in (0,3) uu(3,oo) Then answer the following questions Find the Maximum possible number of solutions of f(x)=|x|

Find the least value of f(x)=ax+(b)/(x) where a>0,quad b>0 and x>0