Final answer:
To find the value of b such that the average value of the function f(x) = 6x^2 - 30x + 44 on the interval (0, b) is equal to 17, you need to calculate the definite integral of f(x) over this interval and set it equal to 17 * (b - 0). By finding the antiderivative of f(x), you can then substitute the boundary values 0 and b into the antiderivative expression and calculate the difference. To solve for b, you can set this difference equal to 17 * (b - 0) and solve the resulting equation.
Step-by-step explanation:
To find the value of b such that the average value of the function f(x) = 6x^2 - 30x + 44 on the interval (0, b) is equal to 17, we need to calculate the definite integral of f(x) over this interval and set it equal to 17 * (b - 0).
By finding the antiderivative of f(x), we can then substitute the boundary values 0 and b into the antiderivative expression and calculate the difference. To solve for b, we can set this difference equal to 17 * (b - 0) and solve the resulting equation.
Let me know if you need help with the step-by-step calculations!