AP EAMCET · Maths · Application of Derivatives
Find the value of ' \(p\) ' and ' \(q\) ' if the function \(f(t)=t^3-6 t^2+p t+q\) defined on \([1,3]\) satisfies the Rolle's theorem for \(c=\frac{2 \sqrt{3}+1}{\sqrt{3}}\)
- A \(p \in \mathrm{R}, q=11\)
- B \(p=11, q \in \mathrm{R}\)
- C \(p \in R, q \in R\)
- D \(p=11, q=11\)
Answer & Solution
Correct Answer
(B) \(p=11, q \in \mathrm{R}\)
Step-by-step Solution
Detailed explanation
It is given that, function \(f(t)=t^3-6 t^2+p t+q\) defined on \([1,3]\) satisfied the Rolle's theorem, so \(\begin{gathered} f(1)=f(3) \\ \Rightarrow \quad 1-6+p+q=27-54+3 p+q \\ \Rightarrow \quad 2 p=22 \Rightarrow p=11 \text { and } q \in \mathbf{R} . \end{gathered}\) Hence,…
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