Find the degree two polynomial function f(x) for which it is known that f(0) = 1, f(1) = 5, f(2) = 11.

Find the polynomial function f(x) for which it is known that f(0) = 1, f(1) = 2, f(2) = 11 and f(3) = 34.

Find the polynomial function f(x) for which it is known that f(0) = 1, f(1) = 2, f(2) = 11 and f(3) = 34.

Find the polynomial function f(x) of degree 3 for which it is known that f(0) = 1, f(1) = 2, f(2) = 11 and f(3) = 34.

f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). f(3) is

Find the derivative of the function f(x)=2x^(2)+3x-5" at "x=-1 . Also prove that f'(0)+3f'(-1)=0 .

Let f(x) be a non-constant twice differentiable function defined on (oo, oo) such that f(x) = f(1-x) and f''(1/4) = 0 . Then (a) f'(x) vanishes at least twice on [0,1] (b) f'(1/2)=0 (c) ∫_{-1/2}^{1/2}f(x+1/2)sinxdx=0 (d) ∫_{0}^{1/2}f(t)e^sinxtdt=∫_{1/2}^{1}f(1−t)e^sinπtdt

If f(x) is a polynomial of degree four with leading coefficient one satisfying f(1)=1, f(2)=2,f(3)=3 .then [(f(-1)+f(5))/(f(0)+f(4))]

Polynomial function f(x) satisfying the condition f(x), f(1/x)=f(x)+f(1/x) . If f(10)=1001, then f(20) is

Let f : (-5,5)rarrR be a differentiable function of with f(4) = 1, f'(4)=1, f(0) = -1 and f'(0) =1 If, g(x)=(f(2f^(2)(x)+2))^(2), then g'(0) equals

Let a function f(x), x ne 0 be such that f(x)+f((1)/(x))=f(x)*f((1)/(x))" then " f(x) can be