5 Steps to a 5 AP Calculus BC 2019
182 STEP 4. Review the Knowledge You Need to Score High Example 2 Find the point on the graph ofy=lnxsuch that the normal line a ...
More Applications of Derivatives 183 Step 3: Write equation of normal. mnormal=4; (2, 1/2) Equation of normal:y− 1 2 =4(x−2), or ...
184 STEP 4. Review the Knowledge You Need to Score High Example 1 Write an equation of the tangent line tof(x)=x^3 at (2, 8). Us ...
More Applications of Derivatives 185 Example 3 The slope of a function at any point (x,y)is− x+ 1 y . The point (3, 2) is on the ...
186 STEP 4. Review the Knowledge You Need to Score High Sincef′(x)=cosxandf′ ( π 6 ) =cos ( π 6 ) = √ 3 2 , you can use linear a ...
More Applications of Derivatives 187 What is the minimum and maximum acceleration of the particle on 0≤t≤7? v(t)= t^3 3 − 4 t^2 ...
188 STEP 4. Review the Knowledge You Need to Score High Solution: (a) a(t)=v′(t) andv′(t) is the slope of tangent to the graph o ...
More Applications of Derivatives 189 Step 2: Setv(t) anda(t)=0. Setv(t)= 0 ⇒ 3 t^2 − 12 t+ 9 = 0 ⇒3(t^2 − 4 t+3)= 0 ⇒3(t−1)(t−3) ...
190 STEP 4. Review the Knowledge You Need to Score High 9.4 Parametric, Polar, and Vector Derivatives Main Concepts:Derivatives ...
More Applications of Derivatives 191 Position, Speed, and Acceleration When the motion of a particle is defined parametrically, ...
192 STEP 4. Review the Knowledge You Need to Score High Example Find the equation of the tangent line to the curver= 2 +2 sinθwh ...
More Applications of Derivatives 193 the path. The acceleration vector is 〈 d^2 x dt^2 , d^2 y dt^2 〉 and the magnitude of accel ...
194 STEP 4. Review the Knowledge You Need to Score High Step 3: Sincer= 〈 s· √ 2 2 t,3+ s· √ 2 2 t− 16 t^2 〉 , the derivative is ...
More Applications of Derivatives 195 9.5 Rapid Review Write an equation of the normal line to the graphy=exatx=0. Answer: dy dx ...
196 STEP 4. Review the Knowledge You Need to Score High Find the slope of the tangent line to the graph ofr=−3 cosθ. Answer: dr ...
More Applications of Derivatives 197 For which value(s) oft(t 1 ,t 2 ,t 3 ) is: (a) the particle moving to the left? (b) the acc ...
198 STEP 4. Review the Knowledge You Need to Score High The position function of a moving particle on a line iss(t)=sin(t) for ...
More Applications of Derivatives 199 8 7 6 5 4 3 2 1 0123456789 t v v(t) (feet/sec) (seconds) Figure 9.7-1 Find the Cartesian e ...
200 STEP 4. Review the Knowledge You Need to Score High Step 1: Findmtangent. y= ∣∣ x^3 ∣∣ = { x^3 ifx≥ 0 −x^3 ifx< 0 dy dx ...
More Applications of Derivatives 201 (a) Att=t 2 , the slope of the tangent is negative. Thus, the particle is moving to the le ...
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