Critical Numbers of Asymptotes
(1) Given function: f(x) = (x^2)*[e^(12x)]
(a) Find its horizontal asymptotes.
(b) Find its critical numbers.
(c) Find its inflection points.
(2) Given function: f(x) = (x^3) / [(x^2) - 16]
(a) Find its critical numbers.
(b) Find its inflection points.
https://brainmass.com/math/synthetic-geometry/critical-numbers-asymptotes-57085
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(1) Given function: f(x) = (x^2)*[e^(12x)]
(a) Find its horizontal asymptotes.
but
So, y=0 is the only horizontal asymptote
(b) Find its critical numbers.
Since , let f'(x)=0, we get
...
Solution Summary
This shows how to find critical numbers and inflection points of given functions. The critical numbers and inflection on points are determined.
Writting a Curve Graph of an Equation
Sketch a graph of an equation f(x) = (x)/(x^2) + 4) using (meaning work out each and show me your work to getting the answers) intercepts, extrema, asymptotes, symmetry, and also tell if it's concave up or down and the inflection points. Please do the first and second differentiation and tell me how you did it plus show me the graph. I'm getting thrown for a loop about the critical values. 2 and -2 are not critical values, right? If so, are there any?
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