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Find all the values of ‘a’ for which (a + 2)x3 - 3ax2 + 9ax - 1 = 0 decreases monotonically throughout for all real x

Find all the values of ‘a’ for which (a + 2)x3 - 3ax2 + 9ax - 1 = 0 decreases monotonically throughout for all real x

Grade:10

1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
10 years ago
f'(x)=3(a+2)x^2-6ax+9a<0, for all x
a+2<0, a<-2

f''(x)=6(a+2)x-6a=0 , x=0 the maxima of f'(x) should also be less than zero
f'(0)=9a<0

imply a<-2

sher mohammad
b.tech, iit delhi


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