Astrophysics, help with Taylor expansion

[nissanztt90]

Homework Statement

$$f(E) = \left(\frac{E_c}{E} \right)^{1/2} + \frac{E}{kT}$$

Expand this as a Taylor function with the form...

$$f \approx a_0 + a_1(E-E_0) + a_2(E-E_0)$$

Hint being $$a_1$$ will be 0, because $$E_0$$ is a Gamow peak in this case, so slope will be 0.

What I need to do is fine $$a_0$$ and $$a_2$$

Ive never really learned how to do Taylor expansions, so if someone can offer me some guidance, i would appreciate it very much.

Homework Equations

The Attempt at a Solution

 

[NateD]

I found this equation online, which is basically the same as the one given above, but it gives a_0 and a_2 f(E) = a_0 + a_1(E-E_c)+a_2(E-E_c)^2where a_0 = 1/2, a_1=0 , and a_2 = -1/(2kT). I was wondering if this is a valid solution?