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CUET · MATHS · PYQ PAPER 2023

The point at which the tangent to the curve \(y = \sqrt{4x-3} - 1\) has its slope \(\frac{2}{3}\) is:

  1. A (3, 2)
  2. B (1, 3)
  3. C (2, 2)
  4. D (2, 3)
Verified Solution

Answer & Solution

Correct Answer

(A) (3, 2)

Step-by-step Solution

Detailed explanation

\(\frac{dy}{dx} = \frac{1}{2}(4x-3)^{-1/2} \cdot 4 = \frac{2}{\sqrt{4x-3}}\) \(\frac{2}{\sqrt{4x-3}} = \frac{2}{3} \Rightarrow \sqrt{4x-3} = 3\) \(4x-3 = 9 \Rightarrow 4x = 12 \Rightarrow x = 3\) \(y = \sqrt{4(3)-3} - 1 = \sqrt{9} - 1 = 3 - 1 = 2\) Point: \((3, 2)\)