derivative

NOVA                                                   Math 271             Mini-Project 2: Two Cool Curves

Name:____________________________

DIRECTIONS:  SHOW ALL WORK OR OTHERWISE DEMONSTRATE ALL ANSWERS THROUGH YOUR WORK.

Cool Curve 1: 

Consider the function g(x) =  

Step 1:  Find all horizontal tangent lines (if any ) of g(x).  If there are no horizontal tangent lines, explain why there are no horizontal tangent lines.

Step 2:  Find all vertical tangent lines (if any ) of g(x).  If there are no vertical tangent lines, explain why there are no vertical tangent lines.

Step 3:  Find the equation of the tangent line to the curve at x = 2

Step 4:  Graph, using Winplot (or something equivalent) the function, any horizontal and vertical tangent lines, and the tangent line at x = 2.  Label that as Graph 1 and attach to this document.

Cool Curve 2:

Consider the curve  .  

Step 1:  Find all horizontal tangent lines (if any ) of f(x).  If there are no horizontal tangent lines, explain why there are no horizontal tangent lines.

Step 2:  Find all vertical tangent lines (if any ) of f(x).  If there are no vertical tangent lines, explain why there are no vertical tangent lines.

Step 3:  Find the equation of the tangent line to the curve at x = -1

Step 4:  Graph, using Winplot (or something equivalent) the function, any horizontal and vertical tangent lines, and the tangent line at x = -1.  Label that as Graph 2 and attach to this document.