Since we can match up with the given equation to get and
To approximate we plug into
Note that we may reason through part b) in a different way as well. We know that the tangent line approximation to a function at a point "touches" the function at that point, so must be the same as In this case, since the tangent line was was approximated at the point we know that Further, we know that the (constant) slope of the tangent line approximation was defined to be the slope of at We could rewrite in slope-intercept form as and see that its slope is (or we could take the derivative of to find that ). In either case, we see that the equals the slope of the tangent line approximation.