what is the average rate of change of ( f(x) ) from ( x_1=-2 ) to ( x_2 = 3 )? please write your answer…

what is the average rate of change of ( f(x) ) from ( x_1=-2 ) to ( x_2 = 3 )? please write your answer rounded to the nearest hundredth.\n\n( f(x)=sqrt{2x + 9} )

what is the average rate of change of ( f(x) ) from ( x_1=-2 ) to ( x_2 = 3 )? please write your answer rounded to the nearest hundredth.\n\n( f(x)=sqrt{2x + 9} )

Answer

Explanation:

Step1: Calculate (f(x_1)) and (f(x_2))

For (x_1=-2), (f(-2)=\sqrt{2\times(-2)+9}=\sqrt{-4 + 9}=\sqrt{5}\approx2.24) For (x_2 = 3), (f(3)=\sqrt{2\times3+9}=\sqrt{6 + 9}=\sqrt{15}\approx3.87)

Step2: Use the average rate of change formula

The average rate of change formula is (\frac{f(x_2)-f(x_1)}{x_2 - x_1}) Substitute (x_1=-2,x_2 = 3,f(x_1)\approx2.24,f(x_2)\approx3.87) into the formula: (\frac{3.87-2.24}{3-(-2)}=\frac{1.63}{5}=0.326\approx0.33)

Answer:

(0.33)