Question

Calculus A help needed

Answer 1

x f(x) f'(x) f''(x)
0 1 2 4
2 5 0 1
4 11 6 3

Answer 2

Show there is a point c in (0,2) with f'(c) < 0

Answer 3

Assuming \(f(x)\) is continuous and differentiable on [0,2] and (0,2), respectively, you can apply the mean value theorem:
\[f'(c)=\frac{f(2)-f(0)}{2-0}=\frac{1-5}{2}<0\]