F(x) = x^-1, x=.9.

Use linear approximation to estimate answer

Question

F(x) = x^-1, x=.9.

Use linear approximation to estimate answer

anonymous · Answer

I get 

1+(-1)(1-.9)

But that's wrong. PLEASE HELP

misty1212 · Answer

HI!!

anonymous · Answer

HELLO MISTY1212!!

misty1212 · Answer

translate as find the equation for the line tangent to the graph of $y=\frac{1}{x}$ at the point $(1,1)$

misty1212 · Answer

first take the derivative

misty1212 · Answer

you get 
$$f'(x)=-\frac{1}{x^2}$$

misty1212 · Answer

then find the slope at $x=1$ you get $-1$

misty1212 · Answer

you with me so far?

anonymous · Answer

Yep! I think I did all of that correct

misty1212 · Answer

you get 
$$y-1=-(x-1)$$

misty1212 · Answer

or $$y=-(x-1)+1$$

misty1212 · Answer

now replace $x$ by $.9$

misty1212 · Answer

that is all

misty1212 · Answer

$$-(.9-1)+1=.1+1=1.1$$ if my arithmetic is correct

misty1212 · Answer

looks like you switched them somehow

anonymous · Answer

:-( idk it's saying this is wrong but I think it's completely right. 

The formula we were given was

f(a)+f'(a)(x-a)

anonymous · Answer

Yeah I switched it but neither is correct on this website hahaha. But it looks right to me

misty1212 · Answer

did you get $1.1$?

misty1212 · Answer

i will bet $7 on this answer 
maybe more

anonymous · Answer

Pay up!

anonymous · Answer

Appreciate the help but it's saying it's wrong hahah. I know your work is right. Idk :O

anonymous · Answer

As defined in Section 3.11, if f(x) is differentiable at x=a, then the approximating function L(x) = f(a) + f'(a)(x-a) is the linearization of f at a. 

Let f(x)=x^(-1) x0=0.9. 

Find a linearization at a suitably chosen integer a close to x_0 at which the given function and its derivative are easy to evaluate.

L(X) = 

@misty1212 would reading the question change your answer at all? What did we do wrong here lol

misty1212 · Answer

nothing

misty1212 · Answer

clearly the suitable integer is 1

misty1212 · Answer

also clearly it is 
$$L(x)=-(x-1)+1$$

misty1212 · Answer

also clearly since $.9<1$ we should have $\frac{1}{.9}>1$

anonymous · Answer

Ohh it was asking for the formula -(x-1)+1 not for 1.1.

Thanks a ton for the help, sorry for the confusion.