Finding Second and Third Derivative from Graph

[a1234]

Homework Statement

The problem asks to find g'(2), g''(2), and g'''(4).

Homework Equations

and attempt at solution[/B]

The derivative of g(x) is just the function f(x). So g'(2) = f(2) = -2.

I'm not sure how to find g''(2) and g'''(4).
I understand that g''(2) is f'(2), but how do I find the derivative of f from this graph? Same question for g'''(4) = f''(4).

 

[fresh_42]

Why don't you simply compute $g(x)\,$? Just integrate for $1 \leq x \leq 2$ then for $2 \leq x \leq 3\, , \,3\leq x \leq 4$ and $4\leq x \leq 5\,.$ After this you could draw this function and see whether and where it is differentiable and what the values are.

 

[Ray Vickson]

Homework Statement

The problem asks to find g'(2), g''(2), and g'''(4).

Homework Equations

and attempt at solution[/B]

The derivative of g(x) is just the function f(x). So g'(2) = f(2) = -2.

I'm not sure how to find g''(2) and g'''(4).
I understand that g''(2) is f'(2), but how do I find the derivative of f from this graph? Same question for g'''(4) = f''(4).

The graph gives a complete and exact description of the function $f(x)$. You just need to translate the given information into formulas.

 

[a1234]

I think I'm getting somewhere...
g''(2) = f'(2) is DNE because of the sharp curve, where the tangent line is a vertical line.
g'''(4) = f''(4) is 0 because the first derivative is a constant and the second is 0.