Final answer:
The average value of h(x) = -x² - 2x + 3 over the interval -6<=x<=5 is approximately -4.55.
Step-by-step explanation:
The average value of a function over an interval can be found by finding the definite integral of the function over that interval and dividing by the length of the interval. In this case, the function is h(x) = -x² - 2x + 3 and the interval is -6<=x<=5.
To find the average value, we can use the formula:
Average value = (1/(b-a)) * definite integral from a to b of f(x) dx.
Plugging in the values, we have:
Average value = (1/(5-(-6))) * definite integral from -6 to 5 of (-x² - 2x + 3) dx.
Calculating the definite integral and simplifying, we get:
Average value = (1/11) * (-150/3).
Therefore, the average value of h(x) over the interval -6<=x<=5 is approximately -4.55.