Chapter 4 - Applications of the Derivative - 4.1 Linear Approximation and Applications - Exercises - Page 172: 6

$$0.021$$

To estimate $\Delta f = f (3.02) − f (3)$, we fhave $$ f'(x)=\frac{\pi }{3}\sec^2 \frac{\pi x}{3}$$ Now, we have $$\Delta f= f'(3)\Delta x= \frac{\pi }{3}\sec^2 \frac{\pi 3}{3} (0.02)=\frac{\pi }{3}(0.02)=\approx 0.021 $$