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.)
