# Math

posted by .

Use the fact that (125)^1/3 = 5 and the tangent line approximation to estimate (123)^1/3

• Math -

Let the function be y = x^(1/3)
so we know (125, 5) lies on it, we need (123, ?)

dy/dx = (1/3)x^(-2/3)
at (125,5) , dy/dx = 1/75

the tangent equation is y = (1/75)x + b
but (125,5) is on it
5 = (1/75)(125) + b
5 = 5/3 + b
b = 10/3

tangent line at (125,5) is y = (1/75)x + 10/3

so when x = 123
y = 123/75 + 10/3 = 4.9733

(calculator answer for 123^(1/3) is 4.97319

## Similar Questions

1. ### Calculus

Use linear approximation, i.e. the tangent line, to approximate (the 3 is inside the v part if you know what I mean, it's not 3 times sqrt) 3√125.2 as follows: Let f(x) = 3√x. The equation of the tangent line to f(x) at …
2. ### Math

Use linear approximation, i.e. the tangent line, to approximate 1.6^3 as follows: Let f(x) = x ^3. The equation of the tangent line to f(x) at x = 2 can be written as y=12x-16 Using this, we find our approximation for 1.6 ^3 is ?
3. ### Calculus

Use linear approximation, i.e. the tangent line, to approximate 8.4^(1/3) as follows: Let f(x)= x^(1/3) . The equation of the tangent line to f(x) at x=8 can be written in the form y=mx+c where m=1/12 and c=4/3: Using this, find our …
4. ### Calculus

Use linear approximation, i.e. the tangent line, to approximate 8.4^(1/3) as follows: Let f(x)= x^(1/3) . The equation of the tangent line to f(x) at x=8 can be written in the form y=mx+c where m=1/12 and c=4/3: Using this, find our …
5. ### Calculus (Tangent Line Approximation)

Use tangent line approximation to derive an estimate for (1 + x)n , when x is near 0, and n is any real number.
6. ### ap calculus ab

for f(x)=lnx we know that f(e)=1. Use the tangent line at(e,1) to compute the tangent line approximation of f(3). what does the difference between the actual value and the tangent line approximation have to do with the concavity (2nd …
7. ### math

Use linear approximation, i.e. the tangent line, to approximate ((125.1)^(1/3)) as follows: Let f (x)=((x)^(1/3)). The equation of the tangent line to f(x) at x = 125 can be written in the form y = mx+b where m = b =
8. ### Derivatives?

Given that f(-0.5)=2 and f'(-0.5)=4, use a tangent line approximation to estimate f(0). The lesson is not very clear on what a tangent line approximaton is.
9. ### Math

The edge of a cube was found to have a length of 50 cm with a possible error in measurement of 0.1 cm. Based on the measurement, you determine that the volume is 125,000 cm3. Use tangent line approximation to estimate the percentage …
10. ### Calculus - Approximation

Use linear approximation, i.e. the tangent line, to approximate cubed root { 1.1 }. The equation of the tangent line to f(x) at x = 1 can be written in the form y = mx+b. Show your work. Do not use a calculator.

More Similar Questions