CK-12-Calculus

3.4. The Second Derivative Test http://www.ck12.org The example above had only one inflection point. But we can easily come up w ...

http://www.ck12.org Chapter 3. Applications of Derivatives TABLE3.1: Signs of first and second derivatives Information from appl ...

3.4. The Second Derivative Test http://www.ck12.org TABLE3.2: Key intervals f′(x) f′′(x) Shape of graph x<− 1 + − Increasing, ...

http://www.ck12.org Chapter 3. Applications of Derivatives Review Questions Find all extrema using the Second Derivative Test.f ...

3.5. Limits at Infinity http://www.ck12.org 3.5 Limits at Infinity Learning Objectives A student will be able to: Examine end b ...

http://www.ck12.org Chapter 3. Applications of Derivatives Consider the functionf(x) =ln(xx+^1 )and suppose we wish to find limx ...

3.5. Limits at Infinity http://www.ck12.org So we infer that limx→ 0 ln(xx+^1 )=1. For the infinite limit, limx→∞ln(xx+^1 )=1, t ...

http://www.ck12.org Chapter 3. Applications of Derivatives Evaluate limx→ 0 ex−x^1. Solution: Since limx→ 0 (ex− 1 ) =limx→ 0 x= ...

3.5. Limits at Infinity http://www.ck12.org MEDIA Click image to the left for use the URL below. URL: http://www.ck12.org/flx/re ...

http://www.ck12.org Chapter 3. Applications of Derivatives 3.6 Analyzing the Graph of a Function Learning Objectives A student w ...

3.6. Analyzing the Graph of a Function http://www.ck12.org ( 4 ,+∞),and they−intercept is at( 0 ,^12 ). Asymptotes and Limits at ...

http://www.ck12.org Chapter 3. Applications of Derivatives Let’s look at examples of the other representative functions we intro ...

3.6. Analyzing the Graph of a Function http://www.ck12.org f′(x) = 3 x^2 + 4 x− 1 =0 ifx=−^4 ± √ 28 6 =−^2 ± √ 7 These are the ...

http://www.ck12.org Chapter 3. Applications of Derivatives Example 3:Analyzing Radical Functions Consider the functionf(x) =√ 2 ...

3.6. Analyzing the Graph of a Function http://www.ck12.org We note thatfis a continuous function and thus attains an absolute ma ...

http://www.ck12.org Chapter 3. Applications of Derivatives Lesson Summary We summarized the properties of functions, including ...

3.6. Analyzing the Graph of a Function http://www.ck12.org Review Questions Summarize each of the following functions by filling ...

http://www.ck12.org Chapter 3. Applications of Derivatives TABLE3.10:(continued) f(x) =^2 xx− 22 Analysis Inflection points f(x ...

3.6. Analyzing the Graph of a Function http://www.ck12.org f(x) = 1 +cosx on the interval[−π,π] TABLE3.14: f(x) = 1 +cosx Anal ...

http://www.ck12.org Chapter 3. Applications of Derivatives 3.7 Optimization Learning Objectives A student will be able to: Use ...