Graph of a Differentiable Function with f(2)=0 and Opposite Derivative Trends

[Bashyboy]

Homework Statement

Sketch the graph of a differentiable function f such that f(2)=0, f' < 0 for -infinity < x < 2, and
f' > 0 for 2 < x < infinity.

Homework Equations

The Attempt at a Solution

I have answered this question correctly, but what interested me was that in the back of the book it said that individual answers may vary. When I answered this, I immediately thought of a parabola, but I was wondering if an absolute value function would work as well.

 

[SteveL27]

Homework Statement

Sketch the graph of a differentiable function f such that f(2)=0, f' < 0 for -infinity < x < 2, and
f' > 0 for 2 < x < infinity.

Homework Equations

The Attempt at a Solution

I have answered this question correctly, but what interested me was that in the back of the book it said that individual answers may vary. When I answered this, I immediately thought of a parabola, but I was wondering if an absolute value function would work as well.

Is abs differentiable?

 

[Bashyboy]

I would say yes, just when x doesn't equal 2.