power series sum[n=0,infty][(-1)^n x^(2n) / (2n+1)!]

[kapplayer]

The funtion f is defined by the power series
f(x)= the sum n=0 to infiniti ((-1)^nx^(2n))/(2n+1)!

Find f'(0) and f''(0) determine whether f has a local maximum, a local minimum, or neither at x=0

Show that 1-(1/3!0 approximates f(1) with error less than 1/100

Show that y=f(x) is a solution to the differential equation xy' + y = cosx

any help is greatly apprectiated Im stuck

 

[Deleted member 4993]

Re: power series

The funtion f is defined by the power series
f(x)= the sum n=0 to infiniti ((-1)^nx^(2n))/(2n+1)!

Find f'(0) and f''(0) determine whether f has a local maximum, a local minimum, or neither at x=0

Show that 1-(1/3!0 approximates f(1) with error less than 1/100

Show that y=f(x) is a solution to the differential equation xy' + y = cosx

any help is greatly apprectiated Im stuck

Please show us your work/thoughts - indicating exactly where you are stuck - so that we know where to begin to help you.

 

[kapplayer]

Re: power series

thats the problem i dont know were to begin. Is f'(0) for this equation = 0?

 

[Deleted member 4993]

Re: power series

first find f'(x) from the given function.

Then find f'(0) and etc...

 

[Dr. Flim-Flam]

f(0)=1. f' (0) = 0. f" (0)= -1/3. Hence f(x) has a relative max at (0,1) as f" (0) < 0.