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