A) (-2,3)
B) (2,-3)
C) (-2,-3)
D) (2,3)
Correct Answer: A
Solution :
[a]: Given,\[f(x)=5+36x+3{{x}^{2}}-2{{x}^{3}}\] \[\Rightarrow \]\[f'(x)=36+6x-6{{x}^{2}}=6(6+x-{{x}^{2}})\] For increasing or decreasing,\[f'(x)=0\] \[\Rightarrow 6+x-{{x}^{2}}=0\Rightarrow {{x}^{2}}-x-6=0\] \[\Rightarrow (x-3)(x+2)=0\Rightarrow x=3,-2\] \[-\infty <x<-2,f'(x)=(-ve)(-ve)=(+ve)\],Increasing \[-2<x<3,f'(x)=(-ve)(+ve)=(-ve)\], Decreasing \[3<x<\infty ,f'(x)=(+ve)(+ve)=(+ve)\], Increasing \[\therefore \]The interval in which f(x) is decreasing is (-2, 3).You need to login to perform this action.
You will be redirected in
3 sec