- Try out
`tangentline`on the following examples. This part of the lab is intended to help you become more familiar with the concept of the tangent line to a function*f*(*x*) at a point*x*=*a*. Use the given values of*a*along with another value of your choice to find 3 tangent lines for each function. Also, for each function, plot the function and the three tangent lines on the same graph.- with
*a*= 2 and*a*= -3. - with
*a*= 0 and . - with
*a*= 2 and*a*= 1.

- with
- More generally, the graphs of two functions
*f*(*x*) and*g*(*x*) are tangent at*x*=*a*if*f*(*a*) =*g*(*a*) and*f*'(*a*) =*g*'(*a*). For example, the functions and*g*(*x*) =*x*are tangent at*x*=0, but the functions and*q*(*x*) =*x*+1 are not tangent at*x*=0, even though they have the same slope, because*p*(0) = 0 and*q*(0) = 1 so the graphs of*p*and*q*don't intersect at*x*=0.Suppose that and . Determine if the following statements are true or not.

- is tangent to 1/
*f*(*x*) at*x*=-1. - is tangent to
*f*(*x*)*g*(*x*) at*x*=1. - is tangent to
*f*(*x*)/*g*(*x*) at*x*=1. - is tangent to at .

- is tangent to 1/

Tue Sep 24 13:24:30 EDT 1996