To sketch a graph of the function f(v) = v(a - v)(v - 1) in the given range 0 ≤ v ≤ 1, we need to substitute the value of a = 0.25 into the equation. Let's break it down step-by-step:
1. Plug in the value of a: f(v) = v(0.25 - v)(v - 1).
2. Simplify the equation: f(v) = v(0.25v - v^2)(v - 1).
To sketch the graph, we can analyze the behavior of the function for different values of v:
- As v approaches 0, f(v) also approaches 0.
- As v approaches 1, f(v) also approaches 0.
- The function reaches its maximum value when v = 0.25. At this point, f(v) = 0.25 * (0.25 - 0.25^2)(0.25 - 1).
- The function reaches its minimum value when v = 0.5. At this point, f(v) = 0.5 * (0.25 - 0.5^2)(0.5 - 1).
Based on this information, we can plot the graph of the function f(v) = v(0.25 - v)(v - 1) within the given range 0 ≤ v ≤ 1.