Let f (x) = 2x. Use a tangent line approximation to estimate f (3.02).
Wait until the end to round off your answer
Let's take the tangent line to f at x = 3, which is close to .02. Then Δ x = .02. We have
yold = f (3) = 23 = 8.
The derivative of f is
f '(x) = 2x ln 2
so the slope of the tangent line at 3 is
f '(3) = 8 ln 2.
Now we can do the estimation:
We didn't round until the very last step.