JEE PYQ: Application Of Derivatives Question 37
Question 37 - 2020 (05 Sep Shift 2)
If $x = 1$ is a critical point of the function $f(x) = (3x^2 + ax - 2 - a)e^x$, then:
(1) $x = 1$ and $x = -\frac{2}{3}$ are local minima of $f$
(2) $x = 1$ and $x = -\frac{2}{3}$ are local maxima of $f$
(3) $x = 1$ is a local maxima and $x = -\frac{2}{3}$ is a local minima of $f$
(4) $x = 1$ is a local minima and $x = -\frac{2}{3}$ is a local maxima of $f$
Show Answer
Answer: (4)
Solution
$f’(1) = 0 \Rightarrow (3 + a + 6 - 2)e = 0 \Rightarrow a = -7$. $f’(x) = (3x^2 - x - 2)e^x = (3x+2)(x-1)e^x$. Sign change: $x = -\frac{2}{3}$ is local maxima, $x = 1$ is local minima.
BETA
