If f'(x) = |x-2|, which of the following could be the graph of f(x)?

Question

How do I find the graph of the original?

I have a calculus test tomorrow, please help!

Answer 1

Absolute value functions are essentially just two lines, two linear functions. If f' is a linear function, f has to be quadratic. So the graph of f will look like two quadratic functions peiced together, one upside down from the other (since the same is true of the absolute value function.)

Specifically, |x-2| is |x| shifted right 2 units. So the anti-derivative will be a parabola, (1/2)x^2, shifted right two units, and the left half upside-down, (I.e. opening down, while the right side opens up.)