# Do #f(x) = 6 – 10x^2# and #g(x) = 8 – (x – 2)^2 # share any tangent lines?

##### 2 Answers

Yes, they do. The lines are (approximately)

#### Explanation:

**Function #f#**

At a point

# = (6-10a^2)+(-20a)(x-a)# which can be simplified to

**Function #g#
**

At a point

# = (4+4b-b^2)+(4-2b)(x-b)# which can be simplified to

**The lines coincide** when their slopes are the same and their

This leads to

The solutions are

Using the approximations

we get corresponding values of

Using these in

There are two solutions as detailed below

#### Explanation:

The tangent lines to

the equations read

Equating the

and imposing the equality for all

Solving for