Find a second degree polynomial f(x) such that f(1) = 4,f′(1) = 5, and f′′(1) = 1?

Answer 1

Let f(x)=ax^2+bx+c , f'(x)=2ax+b, f''(x)=2a . f''(1)= 1 = 2a , a=1/2. f'(x)=x+b, f'(1) = 5 = 1+b, b=4. f(x)=x^2/2 + 4x + c, f(1)=1/2+4+c =4, c=-1/2.Therefore, f(x) = x^2/2+4x-1/2