Posted by **Michael** on Saturday, October 14, 2006 at 2:14am.

Suppose that you can calculate the derivative of a function using the formula f(x) = 2f(x) + 4x. If the output value of the function at x=4 is 3 estimate the value of the function at 4.012. Linear Approximation right?

I'm not seeing an f'(x) anywhere. Can you retype your question?

By f'(x) I mean "f prime" or the derivative of f(x)

Yes, linear approximation. f(4)=2. f(4.012)= 3*4.012/4

Suppose that you can calculate the derivative of a function using the formula f'(x) = 2f(x) + 4x. If the output value of the function at x=4 is 3 estimate the value of the function at 4.012. Linear Approximation right? Sorry about that.

Yes, it is a linear approximation.

We have

f'(x) = 2f(x) + 4x

with initial condition f(4)=3, so

f'(4) = 2*3 + 4*4 = 22

We want to approximate the value at x=4.012, so dx=.012

Now use

f(x) + f'(x)dx =approx. f(x+dx)

3 + 22*.012 =approx. f(4.012)

## Answer this Question

## Related Questions

- calculus 2 - Suppose that you can calculate the derivative of a function using ...
- calculus - is the function f(x)=x^2 increasing on decreasing at x = -1. can ...
- Calculus - We are calculating the slope of the function f(x) = sqrt(x) at x = 4...
- Math Calculus - Economists use production functions to describe how output of a ...
- Calculus - I finished this problem but I wanted some feedback because I don't ...
- calculus - Calculate the derivative of the function. Then find the value of the...
- Calc 121 - Okay, how would you go about finding the area of a curve from 1 to 4...
- calculus - I have three questions I'm having a terrible time with: 1)Find, if ...
- Calc. checking answer - Determine whether or not each of the following functions...
- Calculus - Find the linear approximation L(x) of the given function at a, and ...