`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.

Let f(x)={(|x^3+x^2+3x+sinx|(3+sin"1/x),x!=0),(0,x=0):} then number of points (where f(x)attains its minimum value) is

If x^2+3x+5=0a n da x^2+b x+c=0 have common root/roots and a ,b ,c in N , then find the minimum value of a+b+ c dot

Let f(x)={8^(1/x),x<0a[x],a in R-{0},xgeq0, (where [.] denotes the greatest integer function). Then (a) f(x) is Continuous only at a finite number of points (b)Discontinuous at a finite number of points. (c)Discontinuous at an infinite number of points. (d)Discontinuous at x=0

Let f(x) = a+ b|x| + c|x|^4 where a, b and continuous are real constants . Then, f(x) is differentiable at x = 0, if

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

A differentiable function f(x) has a relative minimum at x=0. Then the function f=f(x)+a x+b has a relative minimum at x=0 for (a)all a and all b (b) all b if a=0 (c)all b >0 (d) all a >0

Let f(x)=a^2+b x+c where a ,b , c in R and a!=0. It is known that f(5)=-3f(2) and that 3 is a root of f(x)=0. Then find the other root of f(x)=0.

If for a function f(x),f^'(a)=0,f^(' ')(a)=0,f^(''')(a)>0, then at x=a ,f(x) has a (a) minimum value (b) maximum value (c)not an extreme point (d) extreme point

What is the value of b for which the function f(x)=sinx-bx+c is decreasing in the interval (-oo, oo) ?

Consider the polynomial f(x)=a x^2+b x+c dot If f(0)=0,f(2)=2, then the minimum value of int_0^2|f^(prime)(x)|dxi s___