Question

Find Third Taylor Polynomial at x=0 for the function f(x)= 3sqrt(2x+1)

Answer 1

what is the formula for the taylor expansion of a function around x=a ?

Answer 2

so where are you stuck then?

Answer 3

im unsure how to start it.

Answer 4

you need up until the nth derivative term. In your case n=3, so you need\[f(x)\approx f(0)+\frac{f'(0)}{1!}+\frac{f''(0)}{2!}+\frac{f'''(0)}{3!}\]

Answer 5

so you might want to start by getting the values f(0), f'(0), f''(0), and f''(0)