Question

Find all values of x on the graph of f(x) =2x^3 + 6x^2 + 7 at which there is a horizontal tangent line.

Answer 1

I found an example where it set the equation equal to zero and solved, but I'm just a bit confused on how to solve with the two x's? The example only had one x.

Answer 2

Its the first one

Answer 3

Oh, boy. If you don't mind me asking, how so?

Answer 4

The slope of the tangent line is given by the derivative of the function.
So you need to differentiate your function, set it equal to zero, and then solve to find x.

Answer 5

So, differentiated it's f(x) = 6x^2 + 12x, correct?

Answer 6

yes

Answer 7

I solved and I got x=2?

Answer 8

*x=-2

Answer 9

there should be two solutions - you are almost there

Answer 10

\[\begin{align}
6x^2+12x&=0\\
\therefore 6x(x+2)&=0\tag{1}
\end{align}\]
What two values of \(x\) would make equation (1) equal to zero?

Answer 11

It would be 0, correct?

Answer 12

yes, so the two solutions are:
x=0 or x=-2

Answer 13

Got it! Thanks!

Answer 14

yw :)