TS EAMCET · Maths · Functions
\(f:[1,3] \rightarrow R\) is a function defined as \(f(x)=x^3+a x^2+b x\). If \(f(\mathrm{l})-f(3)=0\) and \(f^{\prime}\left(\frac{2 \sqrt{3}+1}{\sqrt{3}}\right)=0\). Then, \(a-b\) is equal to
- A 5
- B -17
- C \(4 \sqrt{3}\)
- D \(-2 \sqrt{3}\)
Answer & Solution
Correct Answer
(B) -17
Step-by-step Solution
Detailed explanation
Given, \(f(x)=x^3+a x^2+b x\) Also, \(f(1)-f(3)=0\) \( \begin{aligned} \Rightarrow & f(1) =f(3) \Rightarrow 1+a+b=27+9 a+3 b \\ \Rightarrow & 8 a+2 b =-26 \end{aligned} \) \(\Rightarrow \quad 4 a+b=-13\) ...(i) Now, \(f^{\prime}(x)=3 x^2+2 a x+b\)…
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