### Home > CALC > Chapter 5 > Lesson 5.1.3 > Problem 5-26

Examine the mystery functions described below. Homework Help ✎

*f*(*x*) has all of the following properties:*f*″(2) < 0,*f*′(2) = 0 and*f*(2) = 1. Assuming the function is continuous, sketch a small portion of the mystery function near*x*= 2. Describe the function at this point.A different mystery function has all of the following properties:

*f*′(5) = 0,*f*′(*x*) > 0 for 4.98 <*x*< 5, and*f*′(*x*) < 0 for 5 <*x*< 5.02. Draw a sketch of*f*(*x*) near*x*= 5 and state a conclusion.

*f* '(2) = 0 means that there COULD be a local maximum or local minimum at *x* = 2.*f* ''(2) < 0 means that *f*(*x*) is concave down at *x* = 2, confirming that *x* = 2 is a local ________________________.

If slope is positive on the left side of a point and negative on the right side, the that point is the location of a local ___________________.