5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book May 9, 2018 10:9 122 STEP 4. Review the Knowledge You Need to Score High Example 1 Find dy dx ify^2 − 7 y+x^2 − ...

MA 3972-MA-Book May 9, 2018 10:9 Differentiation 123 Step 3: Factor out dy dx : dy dx [2(x+y)+2(x−y)− 5 y^4 ]= 5 x^4 − 2 x− 2 y+ ...

MA 3972-MA-Book May 9, 2018 10:9 124 STEP 4. Review the Knowledge You Need to Score High 7.4 Approximating a Derivative Given a ...

MA 3972-MA-Book May 9, 2018 10:9 Differentiation 125 Method 3: Use the slope of the line segment joining the points atx=2 andx=4 ...

MA 3972-MA-Book May 9, 2018 10:9 126 STEP 4. Review the Knowledge You Need to Score High [–2, 4] by [–2, 4] Figure 7.4-2 TIP • R ...

MA 3972-MA-Book May 9, 2018 10:9 Differentiation 127 Example 2 Example 1 could have been done by using implicit differentiation. ...

MA 3972-MA-Book May 9, 2018 10:9 128 STEP 4. Review the Knowledge You Need to Score High TIP • You do not have to answer every q ...

MA 3972-MA-Book May 9, 2018 10:9 Differentiation 129 7.7 L’Hôpital’sRule for Indeterminate Forms Let lim represent one of the li ...

MA 3972-MA-Book May 9, 2018 10:9 130 STEP 4. Review the Knowledge You Need to Score High Findf′(x)iff(x)=ln(3x). Answer: f′(x)= ...

MA 3972-MA-Book May 9, 2018 10:9 Differentiation 131 7.9 Practice Problems Part A The use of a calculator is not allowed. Find t ...

MA 3972-MA-Book May 9, 2018 10:9 132 STEP 4. Review the Knowledge You Need to Score High 7.10 Cumulative Review Problems (Calcul ...

MA 3972-MA-Book May 9, 2018 10:9 Differentiation 133 Rewritey= √ 2 x+ 1 2 x− 1 as y= ( 2 x+ 1 2 x− 1 ) 1 / 2 . Applying first ...

MA 3972-MA-Book May 9, 2018 10:9 134 STEP 4. Review the Knowledge You Need to Score High Method 1: Use the slope of the line seg ...

MA 3972-MA-Book May 9, 2018 10:9 Differentiation 135 d^2 y dx^2 ∣∣ ∣∣ x=π/ 2 =4 cos ( π 2 ) − 2 ( π 2 )( sin ( π 2 )) = 0 − 2 ( ...

MA 3972-MA-Book May 9, 2018 10:9 136 STEP 4. Review the Knowledge You Need to Score High =lim h→ 0 sin ( π 2 ) [cosh−1]+cos ( π ...

MA 3972-MA-Book April 11, 2018 17:21 CHAPTER 8 Big Idea 2: Derivatives Graphs of Functions and Derivatives IN THIS CHAPTER Summa ...

MA 3972-MA-Book April 11, 2018 17:21 138 STEP 4. Review the Knowledge You Need to Score High 8.1 Rolle’s Theorem, Mean Value The ...

MA 3972-MA-Book April 11, 2018 17:21 Graphs of Functions and Derivatives 139 (c, f(c)) (a, f(a)) (b, f(b)) c x y f 0 f′(c) = f(b ...

MA 3972-MA-Book April 11, 2018 17:21 140 STEP 4. Review the Knowledge You Need to Score High d[Differentiate] to find f′(x): f′( ...

MA 3972-MA-Book April 11, 2018 17:21 Graphs of Functions and Derivatives 141 Set 2 3 (x−1)^1 /^3 = 0 ⇒x=1. Note thatfis not diff ...