Use linear approximation, i.e. the tangent line, to approximate 1/.501 as follows: Let f(x)=1/x and find the equation of the tangent line to f(x) at a "nice" point near 0.501 . Then use this to approximate 1/.501 .

Question

Use linear approximation, i.e. the tangent line, to approximate 1/.501   as follows: Let f(x)=1/x   and find the equation of the tangent line to f(x)  at a "nice" point near 0.501 . Then use this to approximate 1/.501  .

freckles · Answer

does 1x really mean 1/x?

freckles · Answer

Well you first need to find f'(x)

freckles · Answer

$$y-f(a)=f'(a)(x-a) \ y=f'(a)(x-a)+f(a) \ f(x) \approx f'(a)(x-a)+f(a) \text{ for values of x near a }$$

freckles · Answer

How about choosing a to be .5 also called a 1/2)
That is a value near .501