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)=?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

Thank you!