Question

Let f(x)=x^2+x+14. What is the value of x for which the tangent line to the graph of y=f(x) is parallel to the x-axis?

Answer 1

the answer is NOT -1

Answer 2

First, take the derivative of the function.

Answer 3

o i messed that up. now im getting -1/2 but its still wrong.

Answer 4

First, what is the derivative of the function? I will guide you through the problem.

Answer 5

2x+1

Answer 6

Ok. So
\[f'(x)=2x+1\]Now, this function represents the slope of the tangent line at any given value of x.

What slope does a line have to have to be parallel to the x-axis?

Answer 7

zero like you said earlier

Answer 8

Alright, so when the slope of the tangent line is 0, that is when the tangent line is parallel to the x-axis.

The derivative of f(x) represents the slope of the tangent line. Therefore, set the f'(x) equal to 0, and then solve for x, and that will give you the answer of \[\frac{-1}{2}\]That is the correct answer, so I'm not sure why it appears as wrong. Make sure you copied down the problem correctly, I suppose.

Answer 9

o it should be "what is the value of f(x)" not "x"

Answer 10

The wording of that question seems strange. I think it means this:
\[f(\frac{-1}{2})=(\frac{-1}{2})^2+\frac{-1}{2}+14=13.75\]Which is the value of f(x) given a value of x where the tangent line is parallel to the x-axis.

Answer 11

yeah, that correct