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< beta), then the interval (alpha,beta)

If f(x)=m x+ca n df(0)=f^(prime)(0)=1. What is f(2)?

If alpha , beta are the roots of x^2 +x+1=0 then alpha beta + beta alpha =

If f(x) is a polynomial such that (alpha+1)f(alpha)-alpha=0AA alpha epsilon Nuu{0}, alpha le n , then

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

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

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) is a polynomial of degree n(gt2) and f(x)=f(alpha-x) , (where alpha is a fixed real number ), then the degree of f'(x) is

Let f(x0 be a non-constant thrice differentiable function defined on (-oo,oo) such that f(x)=f(6-x)a n df^(prime)(0)=0=f^(prime)(x)^2=f(5)dot If n is the minimum number of roots of (f^(prime)(x)^2+f^(prime)(x)f^(x)=0 in the interval [0,6], then the value of n/2 is___

Statement-1 If y=f(x) is increasing in [alpha,beta] , then its range is [f(alpha),f(beta)] Statement-2 Every increasing function need not to be continuous.