TS EAMCET · Maths · Application of Derivatives
If \(4+3 x-7 x^2\) attains its maximum value \(M\) at \(x=\alpha\) and \(5 x^2-2 x+1\) attains its minimum value \(m\) at \(x=\beta\), then \(\frac{28(M-\alpha)}{5(m+\beta)}=\)
- A 28
- B 23
- C 5
- D 1
Answer & Solution
Correct Answer
(B) 23
Step-by-step Solution
Detailed explanation
Let \(f(x)=4+3 x-7 x^2\) \(\begin{aligned} & f^{\prime}(x)=3-14 x=0 \Rightarrow x=\frac{3}{14}=\alpha \\ & f^{\prime \prime}(x)=-14 \lt 0 \end{aligned}\) \(\therefore f(x)\) is maximum at \(x=\frac{3}{14}\) and maximum Value is…
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