Question

Given the function h(x)=x2+6x+6h(x)=x^2+6x+6h(x)=x2+6x+6, determine the average rate of change of the function over the interval −7≤x≤2-7\le x \le 2−7≤x≤2.

Answer 1

Answer:

The answer is -11.

Step-by-step explanation:

The function is given by $h(x) = x^{2} - 6x + 6$.

Rate of change refers to the ratio between the change of the dependent variable with the change of independent variable.

The minimum value of x is -7 and the maximum value is 2.

h(-7) = 49 + 42 + 6 = 97.

h(2) = 4 - 12 + 6 = -2.

The average rate of change is $\frac{h(-7) - h(2)}{-7 - 2} = \frac{97 + 2}{-9} = -11$.