4.3.6 Exercises
1. Consider the function $f(x) = 3x + 4$.
a. Compute $L_4$ and $R_4$ for $y = f(x)$ on the interval $[2, 5]$. Be sure to clearly identify the value of $\Delta x$, as well as the locations of $x_0, x_1, \dots, x_4$. Include a careful sketch of the function and the corresponding rectangles being used in the sum.
b. Use your sketch from above to determine whether $L_4$ is an over or under-estimate. Do the same for $R_4$. Then use a familiar geometric formula to determine the exact value of the area of the region bounded by $y = f(x)$ and the $x$-axis on $[2, 5]$ to verify your answers.