Given the function g(x) = x2 + 5x + 1, determine the average rate of change of the function over the interval -9 < x < -2.

-6

Step-by-step explanation:

The average rate of change of a function, f(x), on interval [a,b] is (f(b)-f(a))/(b-a).

So the avereage rate of change of a function, f(x)=x^2+5x+1, on [-9,-2] is

(f(-2)-f(-9))/(-2--9)

(f(-2)-f(-9))/(7)

Stop!

To find f(-2), you replace x in f(x) = x^2 + 5x + 1, with (-2) giving you f(-2)=(-2)^2+5(-2)+1=4-10+1=-6+1=-5.

To find f(-9), you replace x in f(x) = x^2 + 5x + 1, with (-9) giving you f(-2)=(-9)^2+5(-9)+1=81-45+1=36+1=37.

Continue!

(f(-2)-f(-9))/(7)

=(-5-37)/7

=(-42)/7

=-42/7

=-6

x = 25

step-by-step explanation:

a^2+b^2=c^2

7^2+24^2=c^2

49+576=625

sqrt625=25

x=25

sorry, i can't understand your question. will later if you describe more clearly!

: )