Given the function f(x)=-x^2+6x+17 determine the average rate of change of the function over the interval −3≤x≤7.

2

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

Here [ a, b ] = [ - 3, 7 ] , then

f(b) = f(7 ) = - 7² + 6(7) + 17 = - 49 + 42 + 17 = 10

f(a) = f(- 3) = - (- 3)² + 6(- 3) + 17 = - 9 - 18 + 17 = - 10

average rate of change = = = = 2

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

step-by-step explanation: 4 cause 2+2=4