Q. Given the function h(x)=x2−5x+2, determine the average rate of change of the function over the interval 2≤x≤9.Answer:
Calculate Lower Endpoint: To find the average rate of change of the function h(x)=x2−5x+2 over the interval [2,9], we need to calculate the difference in the function values at the endpoints of the interval and divide by the difference in the x-values.
Calculate Upper Endpoint: First, we calculate the value of h(x) at the lower endpoint of the interval, which is x=2.h(2)=(2)2−5(2)+2=4−10+2=−4.
Find Average Rate of Change: Next, we calculate the value of h(x) at the upper endpoint of the interval, which is x=9. h(9)=(9)2−5(9)+2=81−45+2=38.
Find Average Rate of Change: Next, we calculate the value of h(x) at the upper endpoint of the interval, which is x=9. h(9)=(9)2−5(9)+2=81−45+2=38. Now, we find the average rate of change by subtracting the function value at the lower endpoint from the function value at the upper endpoint and dividing by the difference in x-values. Average rate of change = (h(9)−h(2))/(9−2)=(38−(−4))/(9−2)=42/7=6.