AP CALCULUS BC
Find the Maclaurin polynomial P4 for f(x) = x^2 e^x.
I have the answer, but I would like to see the method of getting it.

Question

AP CALCULUS BC
Find the Maclaurin polynomial P4 for f(x) = x^2 e^x. 
I have the answer, but I would like to see the method of getting it.

anonymous · Answer

$$f(x) = f(0) + x f'(0) + \frac{x^2 f''(0)}{2!} + \frac{x^3 f'''(0)}{3!} + \frac{x^4 f''''(0)}{4!}+...$$

anonymous · Answer

this is the maclaurin series for any function f(x) here $$f'(0) = \frac{d f(x)}{dx} |_{x= 0}$$

anonymous · Answer

P4 is the polynomial till the fourth derivative as shown in the sample equation.

anonymous · Answer

differentiate the given function four times ( to get the four derivatives needed ) 
and plug x = 0 into the obtained derivatives and then substitute those derivatives in the place of f'(0), f''(0), f'''(0) and f''''(0)

anonymous · Answer

any doubts?

anonymous · Answer

Ok, I'm going to do this now on paper and see if I get it.

anonymous · Answer

Ohhhh, ok. I got it!
Parts of the derivatives start cancelling out. I was wondering what happened to the factorials  in the denominator lol. Thanks for clearing it up :)

anonymous · Answer

Its been a pleasure :)