 In this video, we're going to apply the remainder estimation theorem, otherwise known as the Lagrange error bound, to find a bound on the error associated with using the sixth degree Taylor polynomials centered at x equals 0 to approximate the function cosine of x on the interval negative 3 fourths to 3 fourths. Now, according to the theorem, we need to identify a value of m such that it is the maximum value of the seventh derivative of cosine of x on the interval of interest. Now, the seventh derivative of f is sine of x. So let's take a look at the graph of sine of x on the interval negative 3 fourths to 3 fourths. We see that the graph is strictly increasing on that interval. So the maximum value of the absolute value of the seventh derivative of cosine of x on the interval negative 3 fourths to 3 fourths is sine of 3 fourths, which is less than 0.682. So in the theorem, let's let m equal 0.682. So according to the theorem, we have the error bound is bounded above by 0.682 divided by 7 factorial times x minus 0 to the seventh. This 0 is because that's the value we generated the Taylor polynomial about. So the sixth degree Taylor polynomial approximation of cosine of x centered about x equals 0 on the interval from negative 3 fourths to 3 fourths has an error of at most 0.682 over 7 factorial times 3 fourths minus 0 to the seventh, which is less than 0.000181. And this is quite good.