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Applications of Differentiation of Polynomials: Tangents and Normals Questions



1      Find the equation of the tangent to the following curves at the points indicated:
       a      f(x) = x2 − 2x + 5 at x = −1

       b      f(x) = x2 − 7x − 18 at x = 2

       c      f(x) = x2 − x + 4 at x = −2

       d      f(x) = 3x2 − 7x + 2 at x = 3

       e      f(x) = x3 + 6x2 − 7x + 2 at x = 1

       f      f(x) = −2x3 + 5x2 + 2x +12 at x = 0

       g      f(x) =     at x = 1

       h      f(x) =                        at x = 1

2      Find the equation of the normals to the following curves at the points indicated:

       a      f(x) =            at x = 1
       b      f(x) = x3 − 4x2 + 5x + 2 at x = 1

       c      f(x) =                at x = 2

       d      f(x) =             at x = 2

       e      f(x) =                at x = 0
       f      f(x) =                        at x = −1

       g      f(x) =                    at x = 4

       h      f(x) =                       at x = 2

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Equations of Tangents and Normals

  • 1. Applications of Differentiation of Polynomials: Tangents and Normals Questions 1 Find the equation of the tangent to the following curves at the points indicated: a f(x) = x2 − 2x + 5 at x = −1 b f(x) = x2 − 7x − 18 at x = 2 c f(x) = x2 − x + 4 at x = −2 d f(x) = 3x2 − 7x + 2 at x = 3 e f(x) = x3 + 6x2 − 7x + 2 at x = 1 f f(x) = −2x3 + 5x2 + 2x +12 at x = 0 g f(x) = at x = 1 h f(x) = at x = 1 2 Find the equation of the normals to the following curves at the points indicated: a f(x) = at x = 1 b f(x) = x3 − 4x2 + 5x + 2 at x = 1 c f(x) = at x = 2 d f(x) = at x = 2 e f(x) = at x = 0 f f(x) = at x = −1 g f(x) = at x = 4 h f(x) = at x = 2