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Mathematics notes and formula for class 12 chapter 6 application of derivatives

Mathematics notes and formula for class 12 chapter 6 application of derivatives

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1|Page Mathematics Notes for Class 12 chapter 6. Application of Derivatives Tangents and Normals The derivative of the curve y = f(x) is f ‗(x) which represents the slope of tangent and equation of the tangent to the curve at P is where (x, y) is an arbitrary point on the tangent. The equation of normal at (x, y) to the curve is 1. If then the equations of the tangent and normal at (x, y) are (Y – y) = 0 and (X – x) = 0, respectively. 2. If then the equation of the tangent and normal at (x, y) are (X – x) = 0 and (Y – y) = 0, respectively. Slope of Tangent (i) If the tangent at P is perpendicular to x-axis or parallel to y-axis, www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more) 2|Page (ii) If the tangent at P is perpendicular to y-axis or parallel to x-axis, Slope of Normal (ii) If , then normal at (x, y) is parallel to y-axis and perpendicular to x-axis. (iii) If then normal at (x, y) is parallel to x-axis and perpendicular to y-axis. Length of Tangent and Normal (i) Length of tangent, PA = y cosec θ = (ii) Length of normal, (iii) Length of subtangent, (iv) Length of subnormal, www.ncerthelp.com (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more) 3|Page Angle of Intersection of Two Curves Let y = f1(x) and y = f2(x) be the two curves, meeting at some point P (x1, y1), then the angle between the two curves at P (x1, y1) = The angle between the tangents to th ...
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