CK-12-Calculus

3.3. The First Derivative Test http://www.ck12.org Example 2: The function indicated here is strictly increasing on( 0 ,a)and(b, ...

http://www.ck12.org Chapter 3. Applications of Derivatives Note first that we have a relative maximum atx=aand a relative minimu ...

3.3. The First Derivative Test http://www.ck12.org We observe that the slopes of the tangent lines to the graph change from nega ...

http://www.ck12.org Chapter 3. Applications of Derivatives MEDIA Click image to the left for use the URL below. URL: http://www. ...

3.3. The First Derivative Test http://www.ck12.org For problems #7–10: a. Use the First Derivative Test to find the intervals wh ...

http://www.ck12.org Chapter 3. Applications of Derivatives 3.4 The Second Derivative Test Learning Objectives A student will be ...

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 ...