AP EAMCET · Maths · Application of Derivatives
Find the positive value of '' for which the equality holds, where '' and '' are the points of maximum and minimum, respectively, of the function
- A
- B
- C
- D
Answer & Solution
Correct Answer
(B)
Step-by-step Solution
Detailed explanation
Given, a>0 f(x)=2x3-9ax2+12a2x+1 f'x=6x2-18ax+12a2 f'x=6x2-3ax+2a2 f'x=6x-2ax-a. x=a, x=2a f''x=62x-3a f''a=62a-3a<0 f''2a=64a-3a>0 Thus, α=a, β=2a ⇒2α+β=8 ⇒2a+2a=8 ⇒4a=8 ⇒a=2
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