Now, I have to apologize in advance for this question because it's quite a long one as it is 8 parts. The rules say one acedemic question at a time and I assumed that although this has multiple steps, it is still a single problem. Anyways a huge thank you if you could solve this for me. 1. Given the function f(x) = x^2+4x-12/x^2 a) Show your work for finding the derivative, to prove that f′ (x) = −4x+24/x^3 b) Show your work for finding the second derivative to prove that f′′(x) = 8x−72/x^4 c) Find the x and y intercept(s). d) Find the vertical asymptotes and determine the behavior near the asymptote(s). e) Find the horizontal asymptote. f) Find the intervals of increase/decrease and any local maximum/minimum points. You must include a clear interval chart. g) Find the intervals of concavity and any points of inflection. You must include a clear interval chart. h) Sketch the graph. Be sure to clearly plot any key features.
Now, I have to apologize in advance for this question because it's quite a long one as it is 8 parts. The rules say one acedemic question at a time and I assumed that although this has multiple steps, it is still a single problem. Anyways a huge thank you if you could solve this for me.
1. Given the function f(x) = x^2+4x-12/x^2
a) Show your work for finding the derivative, to prove that
f′ (x) = −4x+24/x^3
b) Show your work for finding the second derivative to prove that
f′′(x) = 8x−72/x^4
c) Find the x and y intercept(s).
d) Find the vertical asymptotes and determine the behavior near the asymptote(s).
e) Find the horizontal asymptote.
f) Find the intervals of increase/decrease and any
g) Find the intervals of concavity and any points of inflection. You must include a clear interval chart.
h) Sketch the graph. Be sure to clearly plot any key features.
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