Question

given the function h(x)=-x^2 - 10x + 29, determine the average rate of change of the function over the interval -6 ≤ x ≤ -1.

Explanation:

Step1: Find $h(-6)$

$h(-6)=-(-6)^2 - 10(-6)+29=-36 + 60+29 = 53$

Step2: Find $h(-1)$

$h(-1)=-(-1)^2 - 10(-1)+29=-1 + 10+29 = 38$

Step3: Calculate average rate of change

$\frac{h(-1)-h(-6)}{-1-(-6)}=\frac{38 - 53}{-1 + 6}=\frac{-15}{5}=-3$

Answer:

$-3$