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Q.

Let f:R→R be defined by fx=−55x,                                                              if   x<−52x3−3x2−120x,                               if   −5 ≤x≤42x3−3x2−36x−336,           if  x>4, let A=x∈R,fxis  increasing then A is

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a

−∞,−5∪4,∞

b

−∞,−5∪−4,∞

c

−5,∞

d

−5,−4∪4,∞

answer is D.

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Detailed Solution

f1(x)=-55x<-5 =6x2-6x-120-5≤x≤4 ⇒f1(x)>0∀x∈(-5,-4)=6x2-6x-36 x>4                      ⇒f1(x)>0       ∀x∈(4,∞)    Therefore, the function is increasing in the interval −5,−4∪4,∞
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