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Given the function h(x)=x^(2)-5x+2, determine the average rate of change of the function over the interval 2 <= x <= 9. Answer:

Given the function h(x)=x2−5x+2 h(x)=x^{2}-5 x+2 , determine the average rate of change of the function over the interval 2≤x≤9 2 \leq x \leq 9 .\newlineAnswer:

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Q. Given the function h(x)=x2−5x+2 h(x)=x^{2}-5 x+2 , determine the average rate of change of the function over the interval 2≤x≤9 2 \leq x \leq 9 .\newlineAnswer:
  1. Calculate Lower Endpoint: To find the average rate of change of the function h(x)=x2−5x+2h(x) = x^2 - 5x + 2 over the interval [2,9][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 xx-values.
  2. Calculate Upper Endpoint: First, we calculate the value of h(x)h(x) at the lower endpoint of the interval, which is x=2x = 2.\newlineh(2)=(2)2−5(2)+2=4−10+2=−4h(2) = (2)^2 - 5(2) + 2 = 4 - 10 + 2 = -4.
  3. Find Average Rate of Change: Next, we calculate the value of h(x)h(x) at the upper endpoint of the interval, which is x=9x = 9. h(9)=(9)2−5(9)+2=81−45+2=38h(9) = (9)^2 - 5(9) + 2 = 81 - 45 + 2 = 38.
  4. Find Average Rate of Change: Next, we calculate the value of h(x)h(x) at the upper endpoint of the interval, which is x=9x = 9. h(9)=(9)2−5(9)+2=81−45+2=38h(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 xx-values. Average rate of change = (h(9)−h(2))/(9−2)=(38−(−4))/(9−2)=42/7=6(h(9) - h(2)) / (9 - 2) = (38 - (-4)) / (9 - 2) = 42 / 7 = 6.

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