Consider the function f(x)=x³+x²-6x+1. Find all the points on the graph of f where the tangent line has slope of -1?
2 Answers
Well, if we want to find when the slope of the tangent is -1, let's take a derivative!
Now
This is a quadratic, which we can solve. I did it by manually factoring, but you can also use quadratic formula if you'd like.
So this is solved when
Plugging this into f(x) gives us the positions where the slope is -1:
So our final answer is:
Explanation:
The points at which the tangent line to
Now, let's solve this for
Using the quadratic formula:
So, at