Let `f(x)` be defined as `f(x)={tan^(-1)alpha-5x^2,0ltxlt1 and -6x ,xgeq1` if `f(x)` has a maximum at `x=1,` then find the values of `alpha` .

If f(x)=2x-x^(2) then find the value of f(1)=____.

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 (1) 0 (2) -1/2 (3) -1 (4) 1

If (x^2+x−2)/(x+3) 1) f(x) then find the value of lim_(x->1) f(x)

Let f(x) be a function defined as follows: f(x)=sin(x^2-3x),xlt=0; a n d6x+5x^2,x >0 Then at x=0,f(x) has a local maximum has a local minimum is discontinuous (d) none of these

Let the function be defined as f(x)={4x 0ltxle1 (-4x+5) 1ltxlt2 then lim_(xrarr1)f(x) is :

Let f(x) be a function defined as f(x)={(x^2-1)/(x^2-2|x-1|-1),x!=1 1/2,x=1 Discuss the continuity of the function at x=1.

If the function f is defined by f(x)={(x+2," if" xgt1), (2" if" -1lexle1 ), (x-1 " if" -3ltxlt-1):} find the values of f(0)

If the function f is defined by f(x)={(x+2," if" xgt1), (2" if" -1lexle1 ), (x-1 " if" -3ltxlt-1):} find the values of f(3)

Let f:[-oo,0]->[1,oo) be defined as f(x) = (1+sqrt(-x))-(sqrt(-x) -x) , then

Let f:RtoR be defined by f(x)=x/(1+x^2),x inR . Then the range of f is