5 Steps to a 5 AP Calculus BC 2019
102 STEP 4. Review the Knowledge You Need to Score High Thus, limh→ 0 sin(π/ 2 +h)−sin(π/2) h = limh→ 0 sin(π/2) cosh+cos(π/2) s ...
CHAPTER 7 Big Idea 2: Derivatives Graphs of Functions and Derivatives IN THIS CHAPTER Summary:Many questions on the AP Calculus ...
104 STEP 4. Review the Knowledge You Need to Score High Rolle’s Theorem Iff is a function that satisfies the following three con ...
Graphs of Functions and Derivatives 105 Example 1 If f(x)=x^2 + 4 x−5, show that the hypotheses of Rolle’s Theorem are satisfied ...
106 STEP 4. Review the Knowledge You Need to Score High Example 3 The pointsP(1, 1) andQ(3, 27) are on the curve f(x)=x^3. Using ...
Graphs of Functions and Derivatives 107 TIP • The formula for finding the area of an equilateral triangle isarea=s 2 √ 3 4 where ...
108 STEP 4. Review the Knowledge You Need to Score High 7.2 Determining the Behavior of Functions Main Concepts:Test for Increas ...
Graphs of Functions and Derivatives 109 Example 2 Find the critical numbers off(x)=(x−3)^2 /^5. f′(x)= 2 5 (x −3)−^3 /^5 = 2 5(x ...
110 STEP 4. Review the Knowledge You Need to Score High Example 4 Find the open intervals on whichf(x)=(x^2 −9)^2 /^3 is increas ...
Graphs of Functions and Derivatives 111 [−π,π] by [−2,2] Figure 7.2-7 Using the [[ Zero] function of the calculator, you obtainx ...
112 STEP 4. Review the Knowledge You Need to Score High If f′(x) changes from positive to negative atx=c(f′>0 forx<cand f ...
Graphs of Functions and Derivatives 113 Example 2 Find the relative extrema for the functionf(x)= x^3 3 −x^2 − 3 x. Step 1: Find ...
114 STEP 4. Review the Knowledge You Need to Score High Step 3: Determine intervals. –1 01 The intervals are (−∞,−1), (−1, 0), ( ...
Graphs of Functions and Derivatives 115 concave downward f ′′< 0 f′′< 0 Figure 7.2-14 Figure 7.2-15 Points of Inflection A ...
116 STEP 4. Review the Knowledge You Need to Score High Note that if a point (a,f(a)) is a point of inflection, thenf′′(c)=0orf′ ...
Graphs of Functions and Derivatives 117 Example 2 Using a calculator, find the values ofxat which the graph ofy=x^2 exchanges co ...
118 STEP 4. Review the Knowledge You Need to Score High Step 4: Set up a table. INTERVALS (−∞,2) x= 2 (2,∞) Test Point 0 5 f′′(x ...
Graphs of Functions and Derivatives 119 Step 4: Set up a table. INTERVALS (−∞,1) x= 1 (1,∞) Test Point 0 2 f′′(x) − undefined − ...
120 STEP 4. Review the Knowledge You Need to Score High The graph indicates that (1) f(5)=0, (2) f′(5) < 0, since f is decrea ...
Graphs of Functions and Derivatives 121 Step 4: Critical numbers: f′(x)= 0 ⇒− 42 x=0orx= 0 f′(x) is undefined atx=±5, which are ...
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