We have already seen how to approximate a function using its tangent line. This was the key idea in Euler’s
method. If we know the function value at some point (say f (a)) and the value of the derivative at the same
point (f
(a)) we can use these to find the tangent line, and then use the tangent line to approximate f (x)
for other points x. Of course, this approximation will only be good when x is relatively near a. The tangent
line approximation of f (x) for x near a is called the first degree Taylor Polynomial of f (x) and is:
f (x) ≈ f (a) + f
(a)(x − a)
