AP EAMCET · Maths · Application of Derivatives
If the Rolle's theorem is applicable for the function \(f(x)\) defined by \(f(x)=x^3+P x-12\) on \([0,1]\), then the value of C of the Rolle's theorem is
- A \(\pm \frac{1}{\sqrt{3}}\)
- B \(-\frac{1}{\sqrt{3}}\)
- C \(\frac{1}{\sqrt{3}}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
Rolle's theorem is applicable on \(\begin{aligned} & f(x)=x^3+P x-12 \text { on }[0,1] \\ & \Rightarrow f(0)=f(1) \Rightarrow-12=1+P-12 \Rightarrow P=-1 \end{aligned}\) Now, \(f^{\prime}(c)=3 c^2-1=0 \Rightarrow c=\frac{1}{\sqrt{3}}\) Since,…
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