Two problems dealing with linear approximation and inflection points
Okay here are two problems that have my friends and I stumped as we can't figure out a correct answer.
At the point where x=3 on the curve y = (ax+1)/(x-2) , where a is a constant the slop of the normal is 1/5. Find the value of a.
Its multiple choice and the answers they give us are 1/2, 2, 0, 3, 1/3.
However, I keep getting -5/3 for a.
The function y=x^4 - 4x^3 + 14 has a horizontal inflection at (A, B). The value of A+B is what?
Yet again it is another multiple choice question. The answers given are -10, 0, -39, 14, or none of these. I have a question though. In class we talk about points of inflection but in this question it talks about horizontal inflection. Is there a difference? We haven't touched base at all in class if it is different.
We found two points of inflection and they were (-2, 2) and (0,14) but we don't know which one is the correct answer if any. Its either 0 or 14 or maybe not if we screwed up in our calculations.
Any help would be appreciated.