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` .

Let f(x) be defined as f(x) = {{:(tan^(-1) alpha - 5x^(2),0 lt x lt 1),(-6x,x ge 1):} . If f(x) has a maximum at x = 1, then find the values of alpha .

Let f(x) be defined as f(x)={tan^(-1)alpha-5x^(2),0 =1 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(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 to R be defined by : f(x)={(k-2x",","if "x le -1),(2x+3",","if "x gt-1):}. If f has a local maximum at x = -1, then a possible value of k is :

f(x) = (alpha x)/(x + 1) (x ne -1) , then for what value of alpha , f{f(x)} = x?

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.