List all x values where the graph of f(x) has vertical tangents
goo.gl/photos/iPu1SHA8yyBFTcZj6
At first I said x=-3 but that is a vertical asymptote, not a vertical tangent. Where does this graph have vertical tangents in this case?
looks to me like there is a vertical tangent at x = 2pi/3
Or near x=2, that was pretty easy, can't believe I didn't spot it at first
To determine the x-values where the graph of a function, f(x), has vertical tangents, you need to identify the points on the graph where the slope of the tangent line is undefined or infinite. In calculus, this occurs when the derivative of the function, f'(x), is equal to either positive or negative infinity.
Looking at the provided link, I gather that the graph is an image. Since I cannot access or view external content directly, I am unable to analyze the graph and provide specific x-values where vertical tangents exist. However, I can guide you on how to find those points manually.
To find the x-values on the graph where vertical tangents occur, follow these steps:
1. Open the image link (goo.gl/photos/iPu1SHA8yyBFTcZj6) in a web browser or image viewer.
2. Study the graph and locate any points where the function appears to have a vertical tangent. These points will typically be where the graph has a sharp bend or a vertical point of inflection.
3. Identify the x-coordinate(s) of the points where vertical tangents occur. These are the x-values where you can draw a vertical line that is tangent to the curve.
By applying these steps to the provided graph, you should be able to list the x-values where the graph of f(x) has vertical tangents.