JEE Mains · Maths · STD 12 - 6. Application of derivatives
The sum of the maximum and minimum values of the function \(f(x)=|5 x-7|+\left[x^{2}+2 x\right]\) is the interval \(\left[\frac{5}{4}, 2\right]\), where \([ t ]\) is the greatest integer \(\leq t\) is \(.......\)
- A \(14\)
- B \(15\)
- C \(13\)
- D \(18\)
Answer & Solution
Correct Answer
(B) \(15\)
Step-by-step Solution
Detailed explanation
\( f(x) =|5 x-7|+\left[x^{2}+2 x\right] \) \(=|5 x-7|+\left[(x+1)^{2}\right]-1 \) Critical points of \(f(x)=\frac{7}{5}, \sqrt{5}-1, \sqrt{6}-1, \sqrt{7}-1, \sqrt{8}-1,2\) Maximum or minimum value of \(f(x)\) occur at critical points or boundary points…
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