jee-main 2021 Q74

jee-main · India · session3_20jul_shift1 Stationary points and optimisation Find critical points and classify extrema of a given function

Let $a$ be a real number such that the function $f ( x ) = a x ^ { 2 } + 6 x - 15 , x \in R$ is increasing in $( - \infty , \frac { 3 } { 4 } )$ and decreasing in $\left( \frac { 3 } { 4 } , \infty \right)$. Then the function $g ( x ) = a x ^ { 2 } - 6 x + 15 , x \in R$ has a
(1) local maximum at $x = - \frac { 3 } { 4 }$
(2) local minimum at $x = - \frac { 3 } { 4 }$
(3) local maximum at $x = \frac { 3 } { 4 }$
(4) local minimum at $x = \frac { 3 } { 4 }$

Let $a$ be a real number such that the function $f ( x ) = a x ^ { 2 } + 6 x - 15 , x \in R$ is increasing in $( - \infty , \frac { 3 } { 4 } )$ and decreasing in $\left( \frac { 3 } { 4 } , \infty \right)$. Then the function $g ( x ) = a x ^ { 2 } - 6 x + 15 , x \in R$ has a\\
(1) local maximum at $x = - \frac { 3 } { 4 }$\\
(2) local minimum at $x = - \frac { 3 } { 4 }$\\
(3) local maximum at $x = \frac { 3 } { 4 }$\\
(4) local minimum at $x = \frac { 3 } { 4 }$

Paper Questions

Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29 Q30 Q61 Q62 Q63 Q64 Q65 Q66 Q67 Q68 Q69 Q70 Q71 Q72 Q73 Q74 Q75 Q76 Q77 Q78 Q79 Q80 Q81 Q82 Q83 Q84 Q85 Q86 Q87 Q88 Q89 Q90