taylor approximation help

**tim_mannire** · March 10th 2010, 02:13 PM

Find the second taylor approximation for y=x^(2) .e^(2x)+3

**hollywood** · March 13th 2010, 08:31 AM

You need to differentiate the function y(x) twice to give y'(x) and y''(x). Then the answer is
$y(x) \approx y(x_0) + (x-x_0)y'(x_0) + \frac{1}{2}(x-x_0)^2y''(x_0)$

If you're having trouble with the differentiation:
$y(x)=x^2e^{2x}+3$
$y'(x)=x^2(e^{2x})'+(x^2)'e^{2x}$
and you can finish it from there. The second derivative is really similar to the first.

Post again if you're still having trouble.

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