AP EAMCET · Maths · Application of Derivatives
If \(f(x)=k x^3-9 x^2+9 x+3(k>0)\) is increasing for all \(x\), then
- A \(k \leq 3\)
- B \(k \geq 3\)
- C \(0 < k < 1\)
- D \(1 < k < 3\)
Answer & Solution
Correct Answer
(B) \(k \geq 3\)
Step-by-step Solution
Detailed explanation
\(\because f(x)=k x^3-9 x^2+9 x+3(k>0)\) is increasing for all \(x\). \(\because f(x)\) is increasing, then \(f^{\prime}(x) \geq 0\)…
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