If f(x)=|x-7|+|x-10|+|x-12| has a minimum at x=k, then the value of k is

f(x)={3+|x-k|,x k} has minimum at x=k, then show that |a|>2

Let f:R to R be defined by f(x)={{:(2k-2x",",ifxle-1),(2x+3",",iffxgt-1):} If f has a local minimum at x=-1, then a possible value of k is

If f(x)={([3+|x-k| ,x k]) has minimum at x=k,then (a )|a| 2 (d) |a|>=2

Let f:""RrarrR be defined by f(x)={(k-2x , if xle-1),( 2x+3, if x gt-1):} . If f has a local minimum at x""=""-1 , then a possible value of k is

if F(x)=|x+2|-|x+12| What is the minimum value?

f(x)=2x^(3)-3x^(2)-12x+12 has minimum at the point

The function f(x)=2x^3-3x^2-12x+5 has a minimum at x=

Let f:R rarr R be defined by, f(x)={[k-x;x le-1],[x^(2)+3,,xgt-1] .If f(x) has least value at x=-1 , then the possible value of k is

Let f(x) = |x -1| + |x-2| + |x-3| , match the column I for the value of k column II. {:("Column - I" , " Column -II"),("(A) f(x) = k has no solution " ,"(p) 1 " ),("(B) f(x)=k has only one solution" , "(q) 2"),(" (C) f(x) = k has two solution of same sign " , "(r) 4"),("(D) f(x)= k has two solution of opposite sign" , "(s) 5"),(,"(t) 8"):}

Let alpha,beta(alpha