1 consider the function f dened bythe rst and second

Reference no: EM13372584

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 ?

1931_Limit de?nition of horizontal asymptote2.png

(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.

235_Limit de?nition of horizontal asymptote3.png

(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.

1999_Limit de?nition of horizontal asymptote4.png

(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.

695_Limit de?nition of horizontal asymptote5.png

2. (a) Find the linearization of f (x) = (x + 1)⁴ at a = 1, and use it to approximate (2.01)⁴

(b) Evaluate 1094_Limit de?nition of horizontal asymptote6.png 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.

830_Limit de?nition of horizontal asymptote7.png

864_Limit de?nition of horizontal asymptote8.png

656_Limit de?nition of horizontal asymptote9.png

4. Dierentiate the following functions.

1871_Limit de?nition of horizontal asymptote10.png

2077_Limit de?nition of horizontal asymptote11.png

705_Limit de?nition of horizontal asymptote12.png

5. Evaluate the following de?nite integrals.

1942_Determine the domain1.png

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 aord 240 ft. of fencing material, what is the width y which gives the maximum area of the ?eld?

Reference no: EM13372584

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