Question

Is it possible to have f'(3)=8 and f''(3)=-3, explain why

Answer 1

Correction:
Let f(x)=ax^2+bx+c
f'(x)=2ax+b
f"(x)=2a
f"(3)=-3 (for any value of x) So 2a=-3 => a=-3/2
f'(3)=2a(3)+b=8
-9+b=8 b=17
Therefore f(x)=-(3/2)x^2+17x+C satisfies the given conditions (C=constant)