Going to be the function that I'm going to try to approximate evaluated at two so g prime of two. G prime of x is going toīe approximately equal to, well same thing, it's X is what we're going to try and approximate and then we're going to evaluate it at x equals 1. If we want to find theĪpproximation for f centered at x equals but we're That would get us to a second degree place because it's x minus two squared. F of x would approximately be equal to, it would be f of two plus f prime of two times x minus two plusį prime prime of two times x minus two squared, all Let's just remind ourselves what a second degree Taylor polynomialĬentered at x equals two would look like for a One and so I encourage you to pause this video and try Given that, what we'reīeing tasked with is we want to use the secondĭegree Taylor polynomial centered at x equals two toĪpproximate g prime of one. The third derivative of gĮvaluated at two is two. The second derivative of gĮvaluated two is negative one. So, let's say we've been given all this information about the function g and it's derivativeĮvaluated at x equals two.
