Question

Find the linear approximation L(x) of ln(x)
at the point a = 12?

Answer 1

I got 1/12 when I
found the derivative and plugged in, but I know it's not right

Answer 2

at the point a =12, you have f(a) =ln (12). and f'(x) = 1/x so f'(8) = 1/8
plug them onto the formula \[\huge L(a) = f(a) + f'(a)*(x-a)\]
you have the formula to calculate some value of function near 8.

Answer 3

read more at http://tutorial.math.lamar.edu/Classes/CalcI/LinearApproximations.aspx