CK-12-Calculus

2.7. Linearization and Newton’s Method http://www.ck12.org is a linearization offnearx 0. Example 1: Find the linearization off( ...

http://www.ck12.org Chapter 2. Derivatives f(x)≈ √ 3 2 + 1 2 ( x−π 3 ) ≈ √ 3 2 + x 2 − π 6 ≈x 2 + 0. 343. Figure 10 Newton’s Met ...

2.7. Linearization and Newton’s Method http://www.ck12.org f(x)≈f(x 0 )+f′(x 0 )(x−x 0 ) ≈− 1 +( 4 )(x− 2 ) ≈− 1 + 4 x− 8 ≈ 4 x− ...

http://www.ck12.org Chapter 2. Derivatives Guess the first approximation to a solution of the equationf(x) =0. A graph would be ...

2.7. Linearization and Newton’s Method http://www.ck12.org Figure 11 xn+ 1 =xn−x (^3) n+xn− 1 3 x^2 n+ 1 x 2 = 0. 6 −(^0.^6 ) (^ ...

http://www.ck12.org Chapter 2. Derivatives Review Questions Find the linearization of f(x) =x (^2) + 1 x ata=1. Find the line ...

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 ...