Question

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)