Example 15 - Find point at which tangent to y = root 4x-3 - 1 - Finding point when tangent is parallel/ perpendicular

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  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
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Example 15 Find the point at which the tangent to the curve 𝑦 = ﷐﷮4𝑥−3﷯−1 has its slope ﷐2﷮3﷯ . Given, slope of the tangent to the curve is ﷐2﷮3﷯ We know that Slope of tangent = ﷐𝑑𝑦﷮𝑑𝑥﷯ ﷐2﷮3﷯ = ﷐𝑑𝑦﷮𝑑𝑥﷯ ﷐𝑑𝑦﷮𝑑𝑥﷯ = ﷐2﷮3﷯ ﷐𝑑﷐﷐﷮4𝑥 − 3﷯ − 1﷯﷮𝑑𝑥﷯ = ﷐2﷮3﷯ ﷐1﷮2﷐﷮4𝑥 − 3﷯﷯×4−0 = ﷐2﷮3﷯ ﷐2﷮﷐﷮4𝑥 − 3﷯﷯ = ﷐2﷮3﷯ 3 = ﷐﷮4𝑥−3﷯ ﷐﷮4𝑥−3﷯ = 3 Squaring both sides 4x − 3 = 9 4x = 12 x = 3 Finding y for x = 3 𝑦=﷐﷮4𝑥−3﷯ − 1 =﷐﷮12−3﷯−1 =﷐﷮9﷯−1=3−1=2 Hence, the required point is ﷐𝟑, 𝟐﷯

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