f(x)=(3x2+ax−2−a)ex
f′(x)=(3x2+ax−2−a)ex+ex(6x+a)=ex(3x2+(a+6)x−2)
∵x=1 is a critical point ∴f′(1)=0
∴3+a+6−2=0
a=−7
∴f′(x)=ex(3x2−x−2)=ex(3x2−3x+2x−2)=ex(3x+2)(x−1)
∴ maxima at x=3−2∴ minima at x=1
If x=1 is a critical point of the function f(x)=(3x2+ax−2−a)ex, then
Held on 5 Sept 2020 · Verified 6 Jul 2026.
x=1 and x=−32 are local minima of f
x=1 andx=−32 is a local maxima of f
x=1 is a local maxima andx=−22 is a local minima of f
x=1 is a local minima andx=−32 are local maxima of f
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