Question

Determine the value of a so that the average rate of change of the function J(x) = 3x^2 - ax - 4 over the interval [-1, a] is 10.

Options:
Option 1: 9
Option 2: 11
Option 3: 13
Option 4: 15

Answer 1

To determine the value of a so that the average rate of change of the function J(x) = 3x^2 - ax - 4 over the interval [-1, a] is 10, we can use the formula and solve for a. The value of a is 13.

Step-by-step explanation:

To determine the value of a so that the average rate of change of the function J(x) = 3x^2 - ax - 4 over the interval [-1, a] is 10, we need to find the average rate of change of the function and set it equal to 10. The average rate of change is given by the formula (J(a) - J(-1))/(a - (-1)). Solving for a will give us the value that satisfies the condition. Let's calculate it step by step:

1. Calculate J(a) by substituting a into the function.
2. Calculate J(-1) by substituting -1 into the function.
3. Calculate (J(a) - J(-1)).
4. Calculate (a - (-1)).
5. Set (J(a) - J(-1))/(a - (-1)) = 10 and solve for a.

By solving the equation, we find that a = 13.