Differentiation - Tangents & Normals Practice
Various problems on finding equations of tangents and normals to curves, along with practice exercises and solutions. Topics include gradients, perpendicular lines, points of tangency, and curve characteristics.
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Presentation Transcript
Differentiation Tangents & Normals
Tangents and Normals BAT find the equations of tangents and normals to curves KUS objectives Starter: Find the equation of the line through 3? ?? = ? A (5, 9) with gradient 1.5 3? ? = ? A (5, 9) and B (2, 0) A (5, 9) that is perpendicular to the line 3? 2? = 8 2? + ?? = ?? Rearrange your answers to the form ?? + ?? = ?
Geogebra WB23 WB23 Find the equation of the tangent to the curve ? = 3?2 5? 2 at the point (1, -4)
WB24 Find the equation of the normal to the curve ? = 3?2 5? 2 at the point (1, -4) tangent Normal
WB25 For the graph ? = ? ? Find the gradient at the point (4, 2) Find the equation of the tangent at this point Find the equation of the normal at this point a) b) c)
WB26 9 ?+ 3? where the gradient is equal to 2 9 ?+ 3? at the point (1, 12) a) Find the points on the curve ? = b) Find the equation of the normal to the curve ? =
WB27 The curve C is given by ? = ??2+ ? ? where a and b are constants Given that the gradient of C at the point (1, 1) is 5, find a and b
WB28 1 ?2 the point (-1,1) Find the equation of the tangent to the curve?(?) = Find the coordinates of the point where this tangent meets the curve again
WB29 Find the equations of the normal(s) to the curve ? ? = ?2 3?2+ 4 which are perpendicular to the line ? 24? = 1
WB30 exam Q ?+4 ? 6 ? The curve C has equation ? = a) Find ?? ?? in its simplest form b) Find an equation of the tangent to C at the point where ? = 2 , ? > 0
WB31 exam Q A curve has equation ? = 12?2 15? 2?3 the curve crosses the x-axis at the origin, and the point (2, 2) lies on the curve a) Find the gradient of the curve with equation ? = 12?2 15? 2?3 at point A b) Hence find the equation of the normal to the curve at point A giving your answer in the form ? + ?? + ? = 0, where p and q are integers
KUS objectives BAT find the equations of tangents and normals to curves self-assess One thing learned is One thing to improve is
