ap-calculus-ab 2012 Q84

ap-calculus-ab · Usa · practice-exam Stationary points and optimisation Find concavity, inflection points, or second derivative properties

For $- 1.5 < x < 1.5$, let $f$ be a function with first derivative given by $f ^ { \prime } ( x ) = e ^ { \left( x ^ { 4 } - 2 x ^ { 2 } + 1 \right) } - 2$. Which of the following are all intervals on which the graph of $f$ is concave down?
(A) $(-0.418, 0.418)$ only
(B) $( - 1,1 )$
(C) $( - 1.354 , - 0.409 )$ and $( 0.409,1.354 )$
(D) $( - 1.5 , - 1 )$ and $( 0,1 )$
(E) $( - 1.5 , - 1.354 ) , ( - 0.409,0 )$, and $( 1.354,1.5 )$

For $- 1.5 < x < 1.5$, let $f$ be a function with first derivative given by $f ^ { \prime } ( x ) = e ^ { \left( x ^ { 4 } - 2 x ^ { 2 } + 1 \right) } - 2$. Which of the following are all intervals on which the graph of $f$ is concave down?

(A) $(-0.418, 0.418)$ only

(B) $( - 1,1 )$

(C) $( - 1.354 , - 0.409 )$ and $( 0.409,1.354 )$

(D) $( - 1.5 , - 1 )$ and $( 0,1 )$

(E) $( - 1.5 , - 1.354 ) , ( - 0.409,0 )$, and $( 1.354,1.5 )$

Paper Questions

QFR1 QFR2 QFR3 QFR4 QFR5 QFR6 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q76 Q77 Q78 Q79 Q80 Q81 Q82 Q83 Q84 Q85 Q86 Q87 Q88 Q89 Q90 Q91 Q92