Question

let f be a function defined by f(x)=ax^2+bx+c with the following properties: f(0)=2; f'(2)=10; f''(10)=4. find the values of a, b, and c

Answer 1

So f(0) = 2 = c (Sub x = 0)

f' = 2ax + b -> f'(2) = 10 = 2ax +b etc

U can finish it off, no?

Answer 2

f'(x) = 2ax+b
f''(x) =2a
f(0)=2 c=2
f''(10) = 2a=4. a=2
f'(2) = 4a+b. 4(2)+b=10. b=2
f(x) = 2x^2+2x+2