Question

Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line. (If the function has no horizontal tangent line, enter NONE.)

Answer 1

ANSWER:

(0, 9)

STEP-BY-STEP EXPLANATION:

We have the following function:

$y=x^2+9$

We differentiate with respect to x to calculate the differential of y, like this:

$\begin{gathered} \frac{dy}{dx}=\frac{d}{dx}(x^2+9) \\ \frac{dy}{dx}=2x \end{gathered}$

To find out if there is a horizontal line dy/dx is 0, and we solve for x, just like this:

$\begin{gathered} 0=2x \\ x=0 \end{gathered}$

We substitute in the function and get:

$\begin{gathered} y=0^2+9 \\ y=9 \end{gathered}$

Therefore, it has a horizontal tangent line at the point (0, 9)