Mc Laurin and his derivative.

Question

I've been struggling on this question that ask me to find the tangent line of this Mclaurin sequence in its point $x=7$:

$$f(x) = −3 + 2(x − 7) + 5(x − 7)^5 + o((x − 7)^5)$$

I've been trying to do the first derivative of that but somehow it's not the right answer, could you guys give me a hand with that?

Answer 1

HINT

Remember that

$$f(x)=f(x_0)+f'(x_0)(x-x_0)+...$$

and that the tangent line to $f$ at $x=x_0$ is given by

$$(y-f(x_0))=f'(x_0)(x-x_0)$$