Max/Min of Polynomial Function

[Hollysmoke]

The question is:

Determine the equation of the line tangent to f(x)=4x^3+12x^2-96x wit hthe smallest slope on the interval -4 <= x <= 2.

So I found the derivative and critical numbers to find the max and min but where do I go from there?

 

[Integral]

So you need to find the line with minimum slope. What function gives you the slope? How do you find extremes of a function?

 

[Hollysmoke]

By finding the critical numbers of the derivative and plugging them into the original function, as well as the intervals and finding the lowest number would be the minimum value.