Verified Solution • 2025–26 Session moderate

QJEEM20Madd57: JEE Main 2020 Mathematics - Class 12 JEEM20Madd57 Solution: If x = 1 is a critical point of the function f(x) = (3x 2 + ax…

If x = 1 is a critical point of the function
f(x) = (3x2 + ax – 2 – a)ex , then :

Multiple Choice Options

  • A x = 1 is a local maxima and x = −23- {2 \over 3} is a local minima of f.
  • B x = 1 and x = −23- {2 \over 3} are local maxima of f.
  • C x = 1 and x = −23- {2 \over 3} are local minima of f.
  • D x = 1 is a local minima and x = −23- {2 \over 3} is a local maxima of f.

Step-by-Step Verified Solution

f(x) = (3x2 + ax – 2 – a)ex

∴\therefore f'(x) = ex(6x + a) + (3x2 + ax – 2 – a)ex

= ex(3x2 + x(6 + a) – 2)

f '(x) = 0 at x = 1

⇒\Rightarrow 3 + (6 + a) – 2 = 0

⇒\Rightarrow a = -7

∴\therefore f'(x) = ex(3x2 – x – 2)

= ex(x – 1) (3x + 2) JEE Main 2020 (Online) 5th September Evening Slot Mathematics - Application of Derivatives Question 122 English Explanation
x = 1 is a local minima and x = −23- {2 \over 3} is a local maxima of f.

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