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Question: Answered & Verified by Expert
Let fx=x3-x2+10x-7,x1-2x+log2b2-4,x>1 Then the set of all values of b, for which fx has maximum value at x=1, is:
MathematicsApplication of DerivativesJEE MainJEE Main 2022 (26 Jul Shift 1)
Options:
  • A -6,-2
  • B 2,6
  • C -6,-2)(2,6
  • D -6,-2)(2,6
Solution:
1400 Upvotes Verified Answer
The correct answer is: -6,-2)(2,6

Given, fx=x3-x2+10x-7,x1-2x+log2b2-4,x>1

Now f1=3

For x<1,f'x=3x2-2x+10>0

  fx is increasing

For x>1,f'x<0

  function is decreasing.

So, at x=1 there is a point of maxima

So, limx1+fx=-2+log2b2-4

For maximum value at x=1

3-2+log2 b2-4

32b2-4>0

b[-6,-2)(2,6]

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