Let f(x) be an even function & even degree polynomial such that `f(1/2)=1/2, f(1)=1, f(2)=-3, f(3)=5` then minimum number of points of inflection for f(x) is

Let f(x) is a continuous function such that f(-1) = -2,f(0) = -1,f(1) = 0,f (2) = 1, f(3) = 0,f (4) = -1 and f(5) = 1 then minimum number of roots of f'(x) + xf " (x) = 0 in the interval (-1,5) are

If f(x) is a polynomial function of the second degree such tha f(0)=5, f(-1)=10 and f(1)= 6 then f(x)=_____.

Let f(x) be a fourth degree polynomial with coefficient of x^(4) is 1 is such that f(-1)=1,f(2)=4.f(-3)=9,(4)=16 then find f(1) .

If f(x) is a polynomial even function such that f(x).f(1/x)=f(x)+f(1/x) and f(2)=65 , then f(-3) =

If f(x) is a polynomial of least degree such that f(1)=1,f(2)=(1)/(2),f(3)=(1)/(3),f(4)=(1)/(4) then f(5)=

Let f(x) be a polynomial of degree 3 such that f(3)=1, f'(3)=-1, f''(3)=0, and f'''(3)=12. Then the value of f'(1) is

Let f(x) be a polynomial of degree 3 such that f(3)=1, f'(3)=-1, f''(3)=0, and f'''(3)=12. Then the value of f'(1) is

if f(x) is differentiable function such that f(1) = sin 1, f (2)= sin 4 and f(3) = sin 9, then the minimum number of distinct roots of f'(x) = 2x cosx^(2) in (1,3) is "_______"