Use linear approximation, i.e. the tangent line, to
approximate cube root of 0.8 as follows:
The equation of the tangent line to f (x) at x = 1 can be written in the form y =___?
Using this, we find our
approximation for cube root of 0.8 is = ____?

Question

Use linear approximation, i.e. the tangent line, to
approximate cube root of 0.8 as follows:
The equation of the tangent line to f (x) at x = 1 can be written in the form y =___? 
Using this, we find our
approximation for cube root of 0.8 is = ____?

anonymous · Answer

Can you write tangent line equation?

anonymous · Answer

f(x ) = ³√ x -> f (1) = 1
f '(x) = 1/3 x ^(2/3)  => f '(1) = 1/3
Tangent line:
y = 1/3 ( x - 1) + 1
   =  x/3   + 2/3
Thus f ( .8 ) = 1/3 ( .8 + 2) =  2.8/ 3 = .7

anonymous · Answer

Oops, 
= .933333

anonymous · Answer

Pls give the feedback, so at least we know the result of our work!

anonymous · Answer

@Chlorophyll is right. I dont know why but i took the derivative of$$1/\sqrt[3]{x}$$
:)

anonymous · Answer

@myko Our mind just trick us somehow! That's why I always need feed back :)

anonymous · Answer

Yeah...the first answer was correct, but not the second....I'm trying to see why it is .933333

anonymous · Answer

So far thanks for the help chlorophyll!!

anonymous · Answer

@Unam, I often have issue with calculation! 
That's why I asked your feedback about the previous one!

anonymous · Answer

Thanks..you got it right Chlorophyll...the computer needs is too picky about digits! 

Thanks so much!

anonymous · Answer

@Unam, make sure you give out the medal to confirm that our work is correct!

anonymous · Answer

I did press the "best answer," is that what you meant?