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ap10_calculus_ab_form_b_q2

ap10_calculus_ab_form_b_q2 - AP CALCULUS AB 2010 SCORING...

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AP ® CALCULUS AB 2010 SCORING GUIDELINES (Form B) Question 2 © 2010 The College Board. Visit the College Board on the Web: www.collegeboard.com. The function g is defined for 0 x > with ( ) 1 2, g = ( ) ( ) 1 sin , g x x x = + and ( ) ( ) 2 1 1 1 cos . g x x x x ′′ = + (a) Find all values of x in the interval 0.12 1 x at which the graph of g has a horizontal tangent line. (b) On what subintervals of ( ) 0.12, 1 , if any, is the graph of g concave down? Justify your answer. (c) Write an equation for the line tangent to the graph of g at 0.3. x = (d) Does the line tangent to the graph of g at 0.3 x = lie above or below the graph of g for 0.3 1 ? x < < Why? (a) The graph of g has a horizontal tangent line when ( ) 0. g x = This occurs at 0.163 x = and 0.359. x = 2 : ( ) 1 : sets 0 1 : answer g x = (b) ( ) 0 g x ′′ = at 0.129458 x = and 0.222734 x = The graph of g is concave down on ( ) 0.1295, 0.2227 because ( ) 0 g x ′′ < on this interval. 2 : { 1 : answer 1 : justification (c) ( ) 0.3 0.472161 g = − ( ) ( ) 0.3 1 0.3 2 1.546007 g g x dx = + = An equation for the line tangent to the graph of g is ( ) 1.546 0.472 0.3 . y x = 4 : ( ) ( ) 1 : 0.3
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