1. Let's first clarify the problem: you want to find the left, right, and midpoint values for $q_6$ in a numerical method context, likely related to Riemann sums or numerical integration. 2. The left, right, and midpoint values refer to the function values at specific points in the interval partition used to approximate an integral. 3. Suppose the interval is divided into $n$ subintervals, and $q_6$ refers to the 6th subinterval. Let the interval be $[a,b]$ and the width of each subinterval be $\Delta x = \frac{b - a}{n}$. 4. The left endpoint of the 6th subinterval is: $$x_{5} = a + 5\Delta x$$ 5. The right endpoint of the 6th subinterval is: $$x_{6} = a + 6\Delta x$$ 6. The midpoint of the 6th subinterval is: $$m_6 = \frac{x_5 + x_6}{2} = a + \left(5 + \frac{1}{2}\right)\Delta x = a + 5.5\Delta x$$ 7. To find the left, right, and midpoint values for $q_6$, evaluate the function $f(x)$ at these points: - Left value: $f(x_5)$ - Right value: $f(x_6)$ - Midpoint value: $f(m_6)$ 8. This method helps approximate integrals by summing areas of rectangles or trapezoids using these function values. If you provide the function and interval, I can help compute these values explicitly.