Suppose that the derivative of a function satisfies the formula f'(x)=4f(x)+2x. If f(3)=6, use linear approximation to estimate the value of the function at 3.008.
f(3.008)=?

Question

Suppose that the derivative of a function satisfies the formula f'(x)=4f(x)+2x. If f(3)=6, use linear approximation to estimate the value of the function at 3.008. 
f(3.008)=?

anonymous · Answer

your point is $(3,6)$ and your slope is 
$f'(3)=4\times f(3)+2\times 3=4\times 6+6=30$

anonymous · Answer

use the point slope formula to find the equation of the line

anonymous · Answer

$$y-6=30(x-3)$$ then replace $x$ by $3.008$ get 
$$y=30(.008)+6$$ whatever that is

anonymous · Answer

Thank you!