5 Steps to a 5 AP Calculus BC 2019
162 STEP 4. Review the Knowledge You Need to Score High Find a number in the interval (0, 2) such that the sum of the number an ...
Applications of Derivatives 163 container into the cylindrical container at the rate of 15 ft^3 /min, how fast is the water leve ...
164 STEP 4. Review the Knowledge You Need to Score High (Calculator) At what value(s) ofxdoes the tangent to the curvex^2 +y^2 ...
Applications of Derivatives 165 5 m h r 18 12 Figure 8.6-2 Differentiate: dV dt = 4 9 πh^2 dh dt . Substituting known values: − ...
166 STEP 4. Review the Knowledge You Need to Score High Step 2: dA dx = 3 2 ( 2 x− 9 )−^1 /^2 (2)(9−x) +(−1)(3)(2x−9)^1 /^2. = 3 ...
Applications of Derivatives 167 Step 4: Second Derivative Test: d^2 V dx^2 = 24 x−92; d^2 V dx^2 ∣∣ ∣∣ x= 6 =52 and d^2 V dx^2 ∣ ...
168 STEP 4. Review the Knowledge You Need to Score High (See Figure 8.6-7.) xx River (200 – 2x) Figure 8.6-7 Step 1: Area: A=x ...
Applications of Derivatives 169 dθ dt = 0 .197 radian/sec. The angle of elevation is changing at 0.197 radian/sec, 5 seconds aft ...
170 STEP 4. Review the Knowledge You Need to Score High Step 2: Enter:y 1 = 2500 x +. 02 +. 004 ∗x Step 3: Use the [Minimum] fun ...
Applications of Derivatives 171 (See Figure 8.6-12.) y y x (x,0) (0,y) (0.5,4) x l 0 Figure 8.6-12 Step 1: Distance formula: l ...
172 STEP 4. Review the Knowledge You Need to Score High (a) Summarize the information off′on a number line. .5 2.5 decr. incr. ...
Applications of Derivatives 173 Step 2: Enter:y 1 = √ ((x−1)∧ 2 +x∧6). Use the [Minimum] function of the calculator and obtain x ...
CHAPTER 9 Big Idea 2: Derivatives More Applications of Derivatives IN THIS CHAPTER Summary:Finding an equation of a tangent is o ...
More Applications of Derivatives 175 Types of Tangent Lines Horizontal Tangents: ( dy dx = 0 ) . (See Figure 9.1-1.) Figure 9.1- ...
176 STEP 4. Review the Knowledge You Need to Score High [−.5π, π] by [−4, 4] Figure 9.1-4 y=−3 sin 2x; dy dx =−3[cos(2x)]2=−6 co ...
More Applications of Derivatives 177 Set 6x^2 = 6 ⇒x^2 =1orx=±1. Atx=−1,y= 2 x^3 =2(−1)^3 =−2; (−1,−2) is a tangent point. Thus, ...
178 STEP 4. Review the Knowledge You Need to Score High Step 3: Find points of tangency. Aty=0,y^2 −x^2 − 6 x+ 7 =0 becomes−x^2 ...
More Applications of Derivatives 179 Example 5 Using your calculator, find the value(s) ofxto the nearest hundredth at which the ...
180 STEP 4. Review the Knowledge You Need to Score High Normal Lines The normal line to the graph of f at the point (x 1 ,y 1 ) ...
More Applications of Derivatives 181 Normal f Tangent Tangent f Normal Figure 9.1-12 Example 1 Write an equation for each normal ...
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