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Finding Second and Third Derivative from Graph

  • #1
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3

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).
 

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Answers and Replies

  • #2
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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
Ray Vickson
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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.
 
  • #4
56
3
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.
 

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