Determine the points on the curve below where the tangent is horizontal

Question

Curve: y=2x^3 + 15x^2 - 84x + 12

how would I go about answering this?

Answer 1

Hey Anne,

The big idea here is that a derivative creates for you a new function that tells you the slope of a tangent line at any point on your original curve.

So if you want to find horizontal tangent lines, you want a place where the slope of the tangent is zero.

Here's where derivatives come into play.

Take the derivative of your original function, then set it equal to zero.

If you solve this, that will give you all of the x-values where your original curve has horizontal tangent lines!

Hope that helps!

Feel free to reach out with any other questions.