There are three types of points to find on the function, and the great thing is that you already know how to find all of them.
In summary, we're finding where f, f ', and f " are zero or undefined. These will mostly be dots, but there may be asymptotes or holes where f is undefined.
Here's the only thing you need to do that we didn't do earlier: after finding the x-value of a CP or IP, plug that x-value back into the original function f to find the corresponding y-value. In order to graph a point, we need to know both coordinates.
Find and graph all critical points of the function f (x) = 3x^{2} + 4x + 7 |
Find and graph all intercepts, vertical asymptotes, critical points, and inflection points of the function. Label each point with its exact coordinates.
f (x) = e^{x}
Find and graph all intercepts, vertical asymptotes, critical points, and inflection points of the function. Label each point with its exact coordinates.
f (x) = ( x - 2 )^{3}
Find and graph all intercepts, vertical asymptotes, critical points, and inflection points of the function. Label each point with its exact coordinates.
f (x) = (1-x)e^{x}
Find and graph all intercepts, vertical asymptotes, critical points, and inflection points of the function. Label each point with its exact coordinates.
f (x) = x^{2}e^{x} - 4e^{x}
Find and graph all intercepts, vertical asymptotes, critical points, and inflection points of the function. Label each point with its exact coordinates.