find average rate of change from equation\nquestion\ngiven the function $f(x)=-x^{2}+x+3$, determine the…

find average rate of change from equation\nquestion\ngiven the function $f(x)=-x^{2}+x+3$, determine the average rate of change of the function over the interval $0leq xleq7$.\nanswer\nattempt 1 out of 2

find average rate of change from equation\nquestion\ngiven the function $f(x)=-x^{2}+x+3$, determine the average rate of change of the function over the interval $0leq xleq7$.\nanswer\nattempt 1 out of 2

Answer

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = f(x)) over the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}). Here, (a = 0) and (b=7).

Step2: Find (f(0))

Substitute (x = 0) into (f(x)=-x^{2}+x + 3). (f(0)=-(0)^{2}+0 + 3=3)

Step3: Find (f(7))

Substitute (x = 7) into (f(x)=-x^{2}+x + 3). (f(7)=-(7)^{2}+7 + 3=-49 + 7+3=-39)

Step4: Calculate the average rate of change

Using the formula (\frac{f(b)-f(a)}{b - a}), substitute (a = 0), (b = 7), (f(0)=3), and (f(7)=-39). (\frac{f(7)-f(0)}{7-0}=\frac{-39 - 3}{7}=\frac{-42}{7}=-6)

Answer:

(-6)