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` .

The value of a for which the function f(x)={{:(tan^(-1)a -3x^2" , " 0ltxlt1),(-6x" , "xge1):} has a maximum at x=1 , is

Let f(x)={((alpha cotx)/x+beta/x^2 ,, 0<|x|lt=1),(1/3 ,, x=0):} . If f(x) is continuous at x=0 then the value of alpha^2+beta^2 is

Let f: R->R be defined as f(x)=x^2+1 . Find: f^(-1)(10)

If f(x)={{:(,5 tan^(-1)alpha-3x^(2),0 lt x lt 1),(,5x-3,x ge 1):} then find the least integer value of alpha for which f(x) has minima at x=1.

Let f : R to [0, pi/2) be defined by f ( x) = tan^(-1) ( 3x^(2) + 6x + a)". If " f(x) is an onto function . then the value of a si

If alpha,beta are zeroes of polynomial f(x) =x^(2)-p(x+1)-c , then find the value of (alpha+1)(beta+1) .

Let f(x)={sin(pix)/2,0lt=x<1 3-2x ,xgeq1 f(x) has local maxima at x=1 f(x) has local minima at x=1 f(x) does not have any local extrema at x=1 f(x) has a global minima at x=1

Let f(x) be a function defined as follows: f(x)=sin(x^2-3x),xlt=0; and 6x+5x^2,x >0 Then at x=0,f(x) (a) has a local maximum (b) has a local minimum (c) is discontinuous (d) none of these

Let f(x) be a function defined by f(x)=int_(1)^(x)t(t^(2)-3t+2)dt,1ltxlt3 then the maximum value of f(x) is

Let f(x) =(alphax)/(x+1) Then the value of alpha for which f(f(x) = x is