Calculus 1

[AllBus]

Can any one lend a hand?

What values of x, are anti-derivatives of f, non-differentiable?

 

[HallsofIvy]

Can any one lend a hand?

What values of x, are anti-derivatives of f, non-differentiable?

One thing you could do is actually find the anti-derivative. Since the anti-derivative (integral) can be interpreted as "area under the curve", the anti-derivative is just the (signed) area- and for this graph that is just areas of rectangles and triangles.

But if you are given a problem like this, you should know one or more theorems that apply. For example there is the "Fundamental Theorem of Calculus" that says the derivative of the anti-derivative of a function, f, is f itself. Why doesn't that mean that the anti-derivative is always differentiable? What are the conditions on the fundamental theorem?