COMEDK · Maths · 27. Application of Derivatives
Let \(f(x)=a-(x-3)^{8 / 9}\), then maxima of \(f(x)\) is
- A 3
- B \(a-3\)
- C \(a\)
- D None
Answer & Solution
Correct Answer
(C) \(a\)
Step-by-step Solution
Detailed explanation
\((x-3)^{8/9} = \left((x-3)^{1/9}\right)^8 \geq 0\) for all real \(x\), with minimum value \(0\) at \(x = 3\). Therefore \(f(x) = a - (x-3)^{8/9} \leq a\), with maximum value \(a\) at \(x = 3\). Alternatively, \(f'(x) = -\dfrac{8}{9}(x-3)^{-1/9}\), which is undefined at…
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