# Smallest possible slope

1. Mar 21, 2009

### Emethyst

1. The problem statement, all variables and given/known data
What is the smallest possible slope for a tangent line to y=2x^3-6x^2+10x+3 on the interval [-2,2]?

2. Relevant equations
implicit differentation

3. The attempt at a solution
Another question that should be easy, yet that I am finding frustrating. To me what it looks like I need to do is take the derivative of the formula and then find any other critical points to use the Algorithm for Extreme Values. The only problem I seem to be having is finding these other critical points because the derivative will not factor. I know 1 is the value for x I need, because the answer is 4 (found the value for x through simple guess and check), but I do not know how to go about finding it or a similiar value. Any help for this question would be great, thanks in advance.

2. Mar 21, 2009

### yyat

Hi Emethyst!

You want to find the minimum of the derivative (since it is always positive). So you have to look for zeros of the second derivative, not the first.

3. Mar 21, 2009

### Emethyst

Ohh now I see where the 1 came from, thanks for the help yyat, don't think I would've spotted that otherwise