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  1. 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.
    1. tex2html_wrap_inline350 with a = 2 and a = -3.
    2. tex2html_wrap_inline356 with a = 0 and tex2html_wrap_inline360 .
    3. tex2html_wrap_inline362 with a = 2 and a = 1.
  2. 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 tex2html_wrap_inline356 and g(x) = x are tangent at x=0, but the functions tex2html_wrap_inline384 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 tex2html_wrap_inline400 and tex2html_wrap_inline402 . Determine if the following statements are true or not.

    1. tex2html_wrap_inline404 is tangent to 1/f(x) at x=-1.
    2. tex2html_wrap_inline410 is tangent to f(x)g(x) at x=1.
    3. tex2html_wrap_inline410 is tangent to f(x)/g(x) at x=1.
    4. tex2html_wrap_inline422 is tangent to tex2html_wrap_inline424 at tex2html_wrap_inline426 .

Sean O Anderson
Tue Sep 24 13:24:30 EDT 1996