If x=1 is a critical point of the function f (x )= (3x^2+ ax-2-a )e^x, then:

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Accepted Answer

Correct answer: D. (d) JEE Main 2020 f (x )= (3x^2+ ax-2-a )e^x f^ ' (x )= (6x+a )e^x+ (3x^2+ ax-2-a )e^x f^ ' (x )= (3x^2+ (a+6 )x-2 )e^x ∵x=1 is critical point : ∴f^ ' (1 )=0 (3+a+6-2 ) e=0 a=-7 ∴f^ ' (x )= (3x^2-x-2 )e^x = (3x+2 ) (x-1 )e^x + x-y+-2/3+1 ∴x=- 23 is point of local maxima. and x=1 is point of local minima.

$If x = 1 is a critical point of the function f (x) = (3 x^{2} + ax - 2 - a) e^{x}, then:$

Solution

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