Homework Help: Calculus

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)

No one has answered this question yet.

Answer this Question

Related Questions

calculus 2 - Suppose that you can calculate the derivative of a function using ...
calculus - The function f is given by the formula f(x)=6x^3+17x^2+4x+21/x+3 when...
Math Calculus - The function f is given by the formula f(x)=6x^3+17x^2+4x+21/x+3...
Calculus - We are calculating the slope of the function f(x) = sqrt(x) at x = 4...
calculus - Calculate the derivative of the function. Then find the value of the...
Math Calculus - Economists use production functions to describe how output of a ...
calculus - You are given the following function. f(x)= (8+x)/(1-8x) (a) Find the...
calculus - I have three questions I'm having a terrible time with: 1)Find, ...
calculus - Find the derivative of the function using the definition of ...
Calculus - I finished this problem but I wanted some feedback because I don'...

For Further Reading

First Name:
School Subject:
Answer: