## Tangents and Normals to Curves Exercise

1. Find the gradients of the following functions at the points indicated.

 Function Point a f(x) = x2 − 3x − 7 ( 2, -9) b g(x) = x3 + 3x2 − 2x − 7 (1, -5) c h(x) = 2x2 − 4 (-2, 4) d y = 2(x2 + 2x − 1) (4, 46) e y = √ x (4, 2) f y = 3/x2 (2, 0.75)

2. Find the coordinates of the points on the curves below with the given gradients.

 Function Gradient a f(x) = x2 − 5x + 6 7 b g(x) = x2 − 4 3 c h(x) = 2x2 − 3x + 8 5 d y = (x − 4)(x + 3) -3 e y = √ x 1/ 8 f y = 4/x2 1

3. Find the equation of the tangent to the curves of the functions below at the points indicated.

Leave the answer in the form ax + by + c = 0. (Use the gradients from question 1 to help.)

 Function Point a f(x) = x2 − 3x − 7 ( 2, -9) b g(x) = x3 + 3x2 − 2x − 7 (1, -5) c h(x) = 2x2 − 4 (-2, 4) d y = 2(x2 + 2x − 1) (4, 46) e y = √ x (4, 2) f y = 3/x2 (2, 0.75)

4. Find the equation of the normal to the curves of the functions in the table from question 3 at the points indicated.

Leave the answer in the form ax + by + c = 0. (Use the gradients from question 1 to help.)