CK-12-Calculus

http://www.ck12.org CHAPTER 3 Applications of Derivatives Chapter Outline 3.1 Related Rates 3.2 EXTREMA AND THEMEANVALUETHEOREM ...

http://www.ck12.org Chapter 3. Applications of Derivatives 3.1 Related Rates Learning Objectives A student will be able to: Sol ...

3.1. Related Rates http://www.ck12.org x^2 +y^2 =z^2 2 xdxdt+ 2 ydydt= 2 zdzdt. Simplifying, we have Equation 1.xdxdt+ydydt=zdzd ...

http://www.ck12.org Chapter 3. Applications of Derivatives We are familiar with the formulas for Perimeter and Area: P= 2 ∗l+ 2 ...

3.1. Related Rates http://www.ck12.org Solution: We first note that this problem presents some challenges that the other example ...

http://www.ck12.org Chapter 3. Applications of Derivatives HencedVdt =^1275 πh^2 dhdt, and by substitution, 5 =^1275 π( 36 )dhdt ...

3.1. Related Rates http://www.ck12.org A regulation softball diamond is a square with each side of length 60 ft. Suppose a play ...

http://www.ck12.org Chapter 3. Applications of Derivatives 3.2 Extrema and the Mean Value Theorem Learning Objectives A student ...

3.2. Extrema and the Mean Value Theorem http://www.ck12.org Theorem:Iff(c)is an extreme value offfor some open interval ofc,and ...

http://www.ck12.org Chapter 3. Applications of Derivatives Proof:Consider the graph offand secant linesas indicated in the figur ...

3.2. Extrema and the Mean Value Theorem http://www.ck12.org Since we need to havecin the interval( 1 , 4 ),the positive root is ...

http://www.ck12.org Chapter 3. Applications of Derivatives Review Questions In problems #1–3, identify the absolute and local mi ...

3.2. Extrema and the Mean Value Theorem http://www.ck12.org In problems #4–6, find the extrema and sketch the graph. f(x) =−x^2 ...

http://www.ck12.org Chapter 3. Applications of Derivatives 3.3 The First Derivative Test Learning Objectives A student will be a ...

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 ...