Question

Find the average rate of change of the function f(x), given below, from x=1 to x=t. f(x)=−2x2−3x−2 Give your answer in terms of t.

Answer 1

To calculate the average rate of change of the function f(x) from x=1 to x=t, evaluate the function at these points, then divide the change in the function value by the change in x, resulting in the expression (-2t^2 - 3t + 5) / (t - 1).

Step-by-step explanation:

To find the average rate of change of the function f(x) = -2x2 - 3x - 2 from x = 1 to x = t, we calculate the change in the function value divided by the change in x.

The function value at x = 1 is f(1) = -2(1)2 - 3(1) - 2 = -7.

The function value at x = t is f(t) = -2t2 - 3t - 2.

Using the formula for average rate of change:

• Δf/Δx = (f(t) - f(1)) / (t - 1)
• = ((-2t2 - 3t - 2) - (-7)) / (t - 1)
• = (-2t2 - 3t - 2 + 7) / (t - 1)
• = (-2t2 - 3t + 5) / (t - 1)

This expression represents the average rate of change of f(x) in terms of t.