Question

qewrewgt

Answer 1

\[4^3=64 \\ 64^\frac{1}{3}=4\]
\[(64.07)^\frac{2}{3}=(64+.07)^\frac{2}{3}\]
I would use the function
\[f(x)=(64+x)^\frac{2}{3}\] and find that functions tangent line at x=0

Answer 2

or i could use the f(a)+f'(a)(x-a)

Answer 3

that gives you the tangent line

Answer 4

ok

Answer 5

\[y=f(a)+f'(a)(x-a) \\ f(x) \approx f(a)+f'(a)(x-a) \text{ for values of x near a=0}\]

Answer 6

let me know if you need anymore help

Answer 7

i got 16+1/6(x). do i plug in 0 for x?

Answer 8

@freckles

Answer 9

if that is right and you used the function I gave you then to find the approximate value for (64+x)^(2/3)
where x=.07

Answer 10

\[(64+x)^\frac{2}{3} \approx f(a)+f'(a)(x-a) \\ (64+.07)^\frac{2}{3} \approx f(a)+f'(a)(.07-a)\]

Answer 11

I replaced the x's with .07

Answer 12

oh ok so i should get 16.01 which i got the first time i did it

Answer 13

I will check your other work

Answer 14

1/6 is the slope

Answer 15

your tangent line looks great

Answer 16

i said f(x)=x^(2/3) and f(a)=16 and f'(a)=1/6 and so i did 16+(1/6)(.03) and got the same answer

Answer 17

now you plugged in 0.07?
and got \[16+\frac{1}{6} \cdot .07 \\ 16+\frac{.07}{6} \\ 16+\frac{7}{600} \\ \frac{16(600)+7}{600} \\ \frac{9600+7}{600} \\ \frac{9607}{600} \\ \approx 16.01167\]

Answer 18

you put in 0.03?

Answer 19

yeah

Answer 20

ok it looks like you found the tangent line at x=64
\[y-(64)^\frac{2}{3}=\frac{2}{3(64)^\frac{1}{3}}(x-64) \\ y-16=\frac{2}{3(4)}(x-64) \\ y-16=\frac{1}{6}(x-64) \\ y=16+\frac{1}{6}(x-64) \\ f(x) \approx 16+\frac{1}{6}(x-64)\]
and this approximation should be could for values of x near x=64

Answer 21

so since you use \[f(x)=x^\frac{2}{3}\]
you should plug in 64.07 for x

Answer 22

I'm not sure where 0.03 comes from and how you got the same tangent line using a different function then me

Answer 23

so what should i do to solve it? Just use 64.07 instead?

Answer 24

@freckles

Answer 25

well your tangent line for f=x^(2/3) for values near x=64
needs to be fixed
and I sorta did that

Answer 26

this is online hw and it keeps saying im wrong

Answer 27

what are you entering in exactly?

Answer 28

the approximation?