If for some differentiable function `f(alpha)=0a n df^(prime)(alpha)=0,` Statement 1: Then sign of `f(x)` does not change in the neighbourhood of `x=alpha` Statement 2: `alpha` is repeated root of `f(x)=0`

Let f(x) be a differentiable function and f(alpha)=f(beta)=0(alpha

If f(alpha)=0 then alpha is called

If f(alpha)=0 then alpha is called

If alpha and beta are two consecutive roots of f(x) = 0, then

f(alpha)=f'(alpha)=f''(alpha)=0,f(beta)=f'(beta)=f''(beta)=0 and f(x) is polynomial of degree 6, then

If minimum value of function f(x)=(1+alpha^(2))x^(2)-2 alpha x+1 is g(alpha) then range of g(alpha) is

Let f(x)=-ax^2-b|x|-c, -alpha le x lt 0, ax^2+b|x|+c 0 le x le alpha where a,b,c are positive and alpha gt 0, then- Statement-1 : The equation f(x)=0has atleast one real root for x in [-alpha,alpha] Statement-2: Values of f(-alpha) and f(alpha) are opposite in sign.

If f(x)=0 has a repeated root alpha, then another equation having alpha as root is

The value of parameter alpha, for which the function f(x)=1+alpha x,alpha!=0 is the inverse of itself