Afriend runs up to you and excitedly explains that she has found that she has found a function g with the following properties:
g is continuous on [0,1] and differentiable on (0,1)
g(0)=1 and g(1)=5
g'(x) is less than or equal to 3 for all x in (0,1)
explain why you doubt your friend's claim.

Given the start point of (0,1) and (1,5), the average slope is (5-1)/(1-0) = 4.  So the finding that g'(x) for the interval is <=3 cannot be true.  It might be for a small segment but not the entire interval.

1. This is a nonagon. A nonagon is a 9-sided polygon; the figure has 9 sides.

2. This is not a regular polygon. A regular polygon is equiangular and equilateral which means that all of the angles are equal in measure and all of the sides are equal in length. The figure shown does not have equal sides or angles; therefore, it is an irregular polygon.