TS EAMCET · Maths · Application of Derivatives
If the rate of change of the slope of the tangent drawn to the curve \(y=x^3-2 x^2+3 x-2\) at the point \((2,4)\) is k times the rate of change of its abscissa, then \(\mathrm{k}=\)
- A \(2\)
- B \(4\)
- C \(6\)
- D \(8\)
Answer & Solution
Correct Answer
(D) \(8\)
Step-by-step Solution
Detailed explanation
\( \frac{dy}{dx} = 3x^2 - 4x + 3 \) \( \frac{d^2y}{dx^2} = 6x - 4 \) \( k = \frac{d^2y}{dx^2} \Big|_{x=2} = 6(2) - 4 \) \( k = 8 \)
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