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Question

1. You are given $f(x) = \frac{3x^2}{(x+2)^2}$ which has the first and second derivative: $f'(x) = \frac{12x}{(x+2)^3}$ and $f''(x) = \frac{24(1-x)}{(x+2)^4}$. Use $f(x)$ and its first and second derivative to solve the following questions, you must make sure it is clear if you are using $f(x)$, $f'(x)$, or $f''(x)$ for each part. (a) Find the coordinates of all $x$ intercept. (b) Find the coordinates of all $y$ intercept. (c) Find the equation(s) of the vertical asymptote(s). (d) Find the equation(s) of the horizontal asymptote(s). (e) Find the intervals of increasing or decreasing of $f(x)$. (f) Find the $x$ and $y$ coordinates of all local maximum and minimum values. Label each coordinate as a maximum or minimum. (g) Find the intervals of concavity of $f(x)$. (h) Find the $x$ coordinates of the inflection point. (i) Sketch the graph of $f(x)$ using the information from parts 3-10

          1. You are given $f(x) = \frac{3x^2}{(x+2)^2}$ which has the first and second derivative: $f'(x) = \frac{12x}{(x+2)^3}$ and $f''(x) = \frac{24(1-x)}{(x+2)^4}$. Use $f(x)$ and its first and second derivative to solve the following questions, you must make sure it is clear if you are using $f(x)$, $f'(x)$, or $f''(x)$ for each part.
(a) Find the coordinates of all $x$ intercept.
(b) Find the coordinates of all $y$ intercept.
(c) Find the equation(s) of the vertical asymptote(s).
(d) Find the equation(s) of the horizontal asymptote(s).
(e) Find the intervals of increasing or decreasing of $f(x)$.
(f) Find the $x$ and $y$ coordinates of all local maximum and minimum values. Label each coordinate as a maximum or minimum.
(g) Find the intervals of concavity of $f(x)$.
(h) Find the $x$ coordinates of the inflection point.
(i) Sketch the graph of $f(x)$ using the information from parts 3-10

1. You are given f(x) = (3x^2)/((x+2)^2) which has the first and second derivative: f'(x) = (12x)/((x+2)^3) and f”(x) = (24(1-x))/((x+2)^4). Use f(x) and its first and second derivative to solve the following questions, you must make sure it is clear if you are using f(x), f'(x), or f”(x) for each part.
(a) Find the coordinates of all x intercept.
(b) Find the coordinates of all y intercept.
(c) Find the equation(s) of the vertical asymptote(s).
(d) Find the equation(s) of the horizontal asymptote(s).
(e) Find the intervals of increasing or decreasing of f(x).
(f) Find the x and y coordinates of all local maximum and minimum values. Label each coordinate as a maximum or minimum.
(g) Find the intervals of concavity of f(x).
(h) Find the x coordinates of the inflection point.
(i) Sketch the graph of f(x) using the information from parts 3-10

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