Let `f(x)` be a differentiable function and `f(alpha)=f(beta)=0(alpha< beta),` then the interval `(alpha,beta)`

Let f(x) is a polynomial function and f(alpha))^(2) + f'(alpha))^(2) = 0 , then find lim_(x rarr alpha) (f(x))/(f'(x))[(f'(x))/(f(x))] , where [.] denotes greatest integer function, is........

Let f(x) is a polynomial function and f(alpha))^(2) + f'(alpha))^(2) = 0 , then find lim_(x rarr alpha) (f(x))/(f'(x))[(f'(x))/(f(x))] , where [.] denotes greatest integer function, is........

Let f(x) is a polynomial function and f(alpha))^(2) + f'(alpha))^(2) = 0 , then find lim_(x rarr alpha) (f(x))/(f'(x))[(f'(x))/(f(x))] , where [.] denotes greatest integer function, is........

Let f : R rarr R be a differentiable function satisfying f(x) = f(y) f(x - y), AA x, y in R and f'(0) = int_(0)^(4) {2x}dx , where {.} denotes the fractional part function and f'(-3) - alpha e^(beta) . Then, |alpha + beta| is equal to.......

Let f : R rarr R be a differentiable function satisfying f(x) = f(y) f(x - y), AA x, y in R and f'(0) = int_(0)^(4) {2x}dx , where {.} denotes the fractional part function and f'(-3) = alpha e^(beta) . Then, |alpha + beta| is equal to.......

If for some differentiable function f(alpha)=0 and f'(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:[0,4]rarr R be a differentiable function then for some alpha,beta in (0,2)int_(0)^(4)f(t)dt

Let y=f(x) be a thrice differentiable function in (-5,5) .Let the tangents to the curve y=f(x) at (1,f(1)) and (3,f(3)) make angles pi/6 and pi/4 ,respectively with positive "x" -axis.If 27int_(1)^(3)((f'(t))^(2)+1)f''(t)dt=alpha+beta sqrt(3) where alpha,beta are integers,then the value of alpha+beta equals

Let f(x) be an identity function and alpha, beta be the roots of equation x^(2)-5x+9=0 then the value of f(alpha)+f(beta) is equal to