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Math 2413 Graded Homework # 10 GHW10 28 October 2013

Due Monday 11/04/2013 in LectureWork to be done in Blue book per syllabus

Section 4.3: How Derivatives Affect the Shape of a Graph

Section 4.5: Summary of Curve Sketching

1. Let f(x) = x4 + 8x3 + 200.

(a) Find the domain off.

(b) Find the open intervals on whichfis increasing and the open intervals on which f is decreasing. Showyour work.

(c) Find the local maximum and minimum values off, if any. Justify your answers.

(d) Find the open intervals where the graph off is concave upward and the open intervals where the graphoff is concave downward. Show your work.

(e) Find the points of inflection of the graph off, if any. Justify your answers.

(f) Find vertical and horizontal asymptotes off, if any. Justify your answers with limit statements.

(g) Find y-intercepts, if any.(h) Use the information from the previous parts to draw a sketch of the graph off. Label your graph, and

include significant points.

2. Let g(x) = x2 4

x2 9.

(a) Find the domain ofg.

(b) Find the open intervals on which g is increasing and the open intervals on which g is decreasing. Showyour work.

(c) Find the local maximum and minimum values ofg , if any. Justify your answers.

(d) Find the open intervals where the graph ofg is concave upward and the open intervals where the graphofg is concave downward. Show your work.

(e) Find the points of inflection of the graph ofg , if any. Justify your answers.

(f) Find vertical and horizontal asymptotes ofg , if any. Justify your answers with limit statements.

(g) Find x-intercepts and y-intercepts, if any.

(h) Use the information from the previous parts to draw a sketch of the graph ofg. Label your graph, andinclude significant points.

3. Let h(x) = 5x2

3 2x5

3 .

(a) Find the domain ofh.

(b) Find the open intervals on which h is increasing and the open intervals on which h is decreasing. Showyour work.

(c) Find the local maximum and minimum values ofh, if any.(d) Find the open intervals where the graph ofh is concave upward and the open intervals where the graph

ofh is concave downward. Show your work.

(e) Find the points of inflection of the graph ofh, if any. Justify your answers.

(f) Find vertical and horizontal asymptotes ofh, if any. Justify your answers with limit statements.

(g) Find x-intercepts and y-intercepts, if any.

(h) Use the information from the previous parts to draw a sketch of the graph ofh. Label your graph, andinclude significant points.

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4. Let k(x) = x2

4 + 3x+ 4ln x.

(a) Find the domain ofk.

(b) Find the open intervals on which k is increasing and the open intervals on which k is decreasing. Showyour work.

(c) Find the local maximum and minimum values ofk , if any.

(d) Find the open intervals where the graph ofk is concave upward and the open intervals where the graphofk is concave downward. Show your work.

(e) Find the points of inflection of the graph ofk , if any. Justify your answers.

(f) Find vertical and horizontal asymptotes ofk , if any. Justify your answers with limit statements.

(g) Use the information from the previous parts to draw a sketch of the graph ofk. Label your graph, andinclude significant points.

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