Question

What is the average rate of change of the function y=2x²+x+2 [0,1/2]?

A) 1
B) 2
C) 3
D) 4

Answer 1

To find the average rate of change of the function y=2x²+x+2 on the interval [0, 1/2], we subtract the function values at x=0 and x=1/2 and divide by the change in x. The calculation results in an average rate of change of 2, making the correct answer B) 2.

Step-by-step explanation:

The student is asking for the average rate of change of the quadratic function y=2x²+x+2 on the interval [0, 1/2]. To find the average rate of change, we compute the difference in function values at the endpoints and divide by the change in x. The formula for the average rate of change is (f(b)-f(a))/(b-a), where a and b are the endpoints of the interval.

First, we calculate the value of the function at x=0:

• f(0) = 2(0)² + (0) + 2 = 2

Then, the value of the function at x=1/2:

• f(1/2) = 2(1/2)² + (1/2) + 2 = 2(1/4) + 1/2 + 2 = 1/2 + 1/2 + 2 = 3

Now, we find the average rate of change:

• ARC = (f(1/2) - f(0)) / ((1/2) - 0)
• ARC = (3 - 2) / (1/2)
• ARC = 1 / (1/2)
• ARC = 2

The correct answer is B) 2.