# Finding Second and Third Derivative from Graph

Tags:
1. Feb 21, 2017

### a1234

1. The problem statement, all variables and given/known data

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

2. Relevant equations and attempt at solution

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).

#### Attached Files:

• ###### Calculus.PNG
File size:
9.9 KB
Views:
49
2. Feb 21, 2017

### Staff: Mentor

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.

3. Feb 21, 2017

### Ray Vickson

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

4. Feb 21, 2017

### 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.