The function f(x)=x^3-6x^2+ax+b is such that f(2)=f(4)=0. consider two statements :s_1:there exists

The function f(x) =x^(3) - 6x^(2)+ax + b satisfy the conditions of Rolle's theorem on [1,3] which of these are correct ?

The function f(x)= xcos(1/x^2) for x != 0, f(0) =1 then at x = 0, f(x) is

A function f(x) is such that f(x+pi/2)=pi/2-|x|AAx . Find f(pi/2) , if it exists.

Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose the function f is twice differentiable,f(0)=f(1)=0 and satisfies f''(x)-2f'(x)+f(x)gee^(x),x in [0,1] Consider the statements. I. There exists some x in R such that, f(x)+2x=2(1+x^(2)) (II) There exists some x in R such that, 2f(x)+1=2x(1+x)

Consider the function f(x)=(x^(3)-x)|x^(2)-6x+5|, AA x in R , then f(x) is

For the function f given by f(x)=x^2-6x+8 , prove that f\ '\ (5)=4 .

Let f(x)=ln(2+x)-(2x+2)/(x+3) . Statement I The function f(x) =0 has a unique solution in the domain of f(x). Statement II f(x) is continuous in [a, b] and is strictly monotonic in (a, b), then f has a unique root in (a, b).

Consider, f (x) is a function such that f(1)=1, f(2)=4 and f(3)=9 Statement 1 : f''(x)=2" for some "x in (1,3) Statement 2 : g(x)=x^(2) rArr g''(x)=2, AA x in R

If the function f(x)= x^(3)-6x^(2)+ax+b satisfies Rolle's theorem in the interval [1,3] and f'((2sqrt(3)+1)/(sqrt(3)))=0 , then

Consider the function f(x)=|x-2|+|x-5|,c inR. Statement 1: f'(4)=0 Statement 2: f is continuous in [2,5], differentiable in (2,5),