COMEDK · Maths · 27. Application of Derivatives
Let \(f(x)=a+(x-4)^{\frac{4}{9}}\), then minima of \(f(x)\) is
- A 4
- B a
- C a-4
- D None of these
Answer & Solution
Correct Answer
(B) a
Step-by-step Solution
Detailed explanation
\(\because f(x)=a+(x-4)^{4 / 9}\) \(\therefore \quad f^{\prime}(x)=0+\frac{4}{9}(x-4)^{-5 / 9}\) Clearly, at \(x=4, f^{\prime}(x)\) is not defined Hence, \(x=4\) is the point of extremum. \(\because \quad f(4)=a+(4-4)^{4 / 9}=a\) \(\therefore\) The minimum value of \(f(x)\) is…
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