1. ## Equation of the best quadratic approximation?

I'm not sure what to do for this. Here's the problem:

"(a) Find the equation of the best quadratic approximation to $y=ln(x)$ at x=1. The best quadratic approximation has the same first and second derivatives as $y=ln(x)$ at x=1.

(b) Use a computer or calculator to graph the approximation and $y=ln(x)$ on the same set of axes. What do you notice?

(c) Use your quadratic approximation to calculate approximate values for ln(1.1) and ln(2)"

Parts b and c, I don't doubt that they'd be easy after getting part a.
So could someone help me with part a?

2. Originally Posted by Rumor
I'm not sure what to do for this. Here's the problem:

"(a) Find the equation of the best quadratic approximation to $y=ln(x)$ at x=1. The best quadratic approximation has the same first and second derivatives as $y=ln(x)$ at x=1.

(b) Use a computer or calculator to graph the approximation and $y=ln(x)$ on the same set of axes. What do you notice?

(c) Use your quadratic approximation to calculate approximate values for ln(1.1) and ln(2)"

Parts b and c, I don't doubt that they'd be easy after getting part a.
So could someone help me with part a?
Taylor polynomial:

$
f(x)\approx P_2(x)=f(x_0)+(x-x_0)f'(x_0)+\frac{(x-x_0)^2}{2}f''(x_0)
$

CB