. Given the function f(x) = x2+4x-12/x2 a) Show your work for finding the derivative, to prove that f′ (x) = −4x+24/x3 b) Show your work for finding the second derivative to prove that f′′(x) = 8x−72/x4 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.
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Please solve this at a more basic grade 12 level so that I can understand
1. Given the function f(x) = x2+4x-12/x2
a) Show your work for finding the derivative, to prove that
f′ (x) = −4x+24/x3
b) Show your work for finding the second derivative to prove that
f′′(x) = 8x−72/x4
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.
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