The smallest value of the constant `m > 0` for which `f(x)=9mx-1+1/x>=0` for all `x>0,` is

The smallest value of of the constant m gt 0 for which f(x) = 9mx - 1 + (1)/(x)ge 0 for all x gt 0 , is

The values of the constants a , b, c for which the function f(x)={(1+a x)^(1//x), x 0 and b, x=0 may be continuous at x=0, are

Find all 'm' for which f(x)=x^(2)-(m-3)x+m>0 for all values of 'x' in [1,2]

A function f(x) is defined as f(x)=[x^(m)(sin1)/(x),x!=0,m in N and 0, if x=0 The least value of m for which f'(x) is continuous at x=0 is

For x>=0, the smallest value of the function f(x)=(4x^(2)+8x+13)/(6(1+x)), is