TS EAMCET · Maths · Application of Derivatives
For a real number ' \(a\) ', if a real valued function \(f(x)=4 x^3+a x^2+3 x-2\) is monotonic in its domain, then the range of ' \(a\) ' is
- A (-6,6)
- B Empty set
- C (-2,2)
- D (2,4)
Answer & Solution
Correct Answer
(A) (-6,6)
Step-by-step Solution
Detailed explanation
\(f'(x) = 12x^2 + 2ax + 3\) For monotonicity, \(D \le 0\) \((2a)^2 - 4(12)(3) \le 0\) \(4a^2 - 144 \le 0\) \(a^2 \le 36\) \(-6 \le a \le 6\)
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