Find the average rate of change of the function between the given values of x. y = 9+ 5x + 0.5x2 between x = 2 and x = 4.
Accepted Solution
A:
Answer:The average rate of change is 8.Step-by-step explanation:The formula to calculate the average rate of change of a function F(x) is:[tex]\frac{F(b)-F(a)}{b-a}[/tex]In this case, F(x) = [tex]0.5x^{2} +5x+9[/tex]a=2 and b=4You have to evaluate x=2 (which is a in the formula) and x=4 (which is b in the formula) in the function.In order to obtain F(b) and F(a) you have to replace x=4 and x=2 in the given function:F(b) = [tex](0.5)4^{2} + 5(4) +9= 37[/tex]F(a) = [tex](0.5)2^{2} + 5(2)+9=21[/tex][tex]\frac{F(b)-F(a)}{b-a} = \frac{37-21}{4-2}=\frac{16}{2} = 8[/tex]The answer is 8.