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Last updated at April 19, 2021 by Teachoo

Example 15 Find the point at which the tangent to the curve π¦ = β(4π₯β3)β1 has its slope 2/3 . Given, Slope of the tangent to the curve is 2/3 We know that Slope of tangent = π π/π π 2/3 = ππ¦/ππ₯ ππ¦/ππ₯ = 2/3 π(β(4π₯ β 3) β 1)/ππ₯ = 2/3 1/(2β(4π₯ β 3)) Γ4β0 = 2/3 2/β(4π₯ β 3) = 2/3 3 = β(4π₯β3) β(ππβπ) = 3 Squaring both sides 4x β 3 = 9 4x = 12 x = 3 Finding y for x = 3 π¦=β(4π₯β3) β 1 =β(12β3)β1 =β9β1 =3β1 =π Hence, the required point is (π, π)