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Q.

Let ‘a’ be a real number such that the function  f(x)=ax2+6x-15 xR is increasing in  -,34 and decreasing in 34, then the function g(x)=ax2-6x+15, xR has a: 

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a

Local minimum at  x=34
 

b

Local minimum at x=-34

 

c

Local maximum at  x=34
 

d

Local maximum at  x=-34
 

answer is D.

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Detailed Solution

fx=ax2+6x-15 f1x=2ax+6 fx is increasing f1x>0 2ax+6>0 a<0 -2ax+6>0 x<3a

a=-4 gx=-4x2-6x+15 g1x=-8x-6

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gx is max at x=-34

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