AP EAMCET · Maths · Application of Derivatives
If \(f(x)=3 x+\frac{12}{x}\) is continuous on \(\mathbb{R}-\{0\}\) and \(M\) is its maximum value, then \(\lim _{x \rightarrow M}(f x)=\)
- A 37
- B -37
- C 2
- D -2
Answer & Solution
Correct Answer
(B) -37
Step-by-step Solution
Detailed explanation
\(\because f(x)=3 x+\frac{12}{x} \Rightarrow f^{\prime}(x)=3-\frac{12}{x^2}\) For critical point: \(f^{\prime}(x)=0\) \(\begin{aligned} & \Rightarrow 3-\frac{12}{x^2}=0 \Rightarrow x^2=4 \Rightarrow x=-2,2 \\ & f^{\prime \prime}(x)=\frac{24}{x^3}\end{aligned}\) At…
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