JEE Mains · Maths · STD 12 - 6. Application of derivatives
The maximum slope of the curve \(y=\frac{1}{2} x^{4}-5 x^{3}+18 x^{2}-19 x\) occurs at the point
- A \((2,2)\)
- B \((0,0)\)
- C \((2,9)\)
- D \(\left(3, \frac{21}{2}\right)\)
Answer & Solution
Correct Answer
(A) \((2,2)\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=2 x^{3}-15 x^{2}+36 x-19\) Since, slope is maximum so, \(\frac{ d ^{2} y }{ dx ^{2}}=6 x ^{2}-30 x +36=0\) \(\Rightarrow x^{2}-5 x+6=0\) \(x=2,3\) at \(x=2\) \(\frac{ d ^{3} y }{ dx ^{3}}=12 x -30\) at \(x=2, \frac{d^{3} y}{d x^{3}}< 0\) So, maxima…
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