Reference no: EM13108111
1. Consider the function f de?ned by
The ?rst and second derivatives of f are
(a) Determine the domain of f . Write your answer in interval notation.
(b) What are the x-intercept(s) of the graph of f ? What are the y-intercept(s) of the graph of f ?
(c) Find each horizontal asymptote of the graph of f , if any exists, by using the limit de?nition of horizontal asymptote.
(d) Find each vertical asymptote of the graph of f , if any exists, by using the limit de?nition of vertical asymptote.
(e) Find where f is increasing, and where f is decreasing? Write your answer in interval notation.
(f) Find critical points of f and classify each as a local maximum, a local minimum, or neither.
(g) Determine where the graph of f concave up, and where the graph of f concave down? Write your answer in interval notation.
(h) sketch the graph f.
2. (a) Find the linearization of f (x) = (x + 1)4 at a = 1, and use it to approximate (2.01)4
(b) Evaluate 
dx by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and ?nd the area using high school geometry.
3. Evaluate the following limits using L'Hospital's Rule.
4. Di erentiate the following functions.
5. Evaluate the following de?nite integrals.
6. A farmer wants to fence o a rectangular ?eld and then divide the ?eld in half with a fence down the middle (see diagram below). If he can only a ord 240 ft. of fencing material, what is the width y which gives the maximum area of the ?eld?
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: A farmer wants to fence o a rectangular ?eld and then divide the ?eld in half with a fence down the middle (see diagram below). If he can only a ord 240 ft. of fencing material, what is the width y which gives the maximum area of the ?eld?
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