Smallest Possible Slope for Tangent Line to y=2x^3-6x^2+10x+3 on Interval [-2,2]

[Emethyst]

Homework Statement

What is the smallest possible slope for a tangent line to y=2x^3-6x^2+10x+3 on the interval [-2,2]?

Homework Equations

implicit differentation

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 similar value. Any help for this question would be great, thanks in advance.

 

[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.

 

[Emethyst]

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