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`

If one root of the equation (alpha-4)x^2+2x+1=0 is 1, then alpha =

Suppose that f(0)=0a n df^(prime)(0)=2, and let g(x)=f(-x+f(f(x)))dot The value of g' (0) is equal to _____

Let alpha,beta be the roots of x^(2)-2xcosphi+1=0 , then the equation whose roots are alpha^(n),beta^(n) is

If f((x+2y)/3)=(f(x)+2f(y))/3AAx ,y in Ra n df^(prime)(0)=1,f(0)=2, then find f(x)dot

Suppose that f(x) is a differentiable function such that f'(x) is continuous, f'(0)=1 and f''(0) does not exist. Let g(x) = xf'(x). Then

Suppose that f(x) is a differentiable function such that f'(x) is continuous, f'(0)=1 and f''(0) does not exist. Let g(x)=xf'(x) . Then-

Suppose that f(x) is a differentiable function such that f'(x) is continuous, f'(0) = 1 and f"(0) does not exist. Let g(x) = xf'(x). Then

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(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___

IF alpha and beta be the roots of the equation 2x^2+x+1=0 find the equation whose roots are alpha^2/beta and beta^2/alpha