f(x)=x^{2}+10\nover which interval does f have a positive average rate of change?\nchoose 1 answer:\na…

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function (f(x)) over the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}).

Step2: Calculate for option A ([-1,2])

First, find (f(-1)) and (f(2)). (f(-1)=(-1)^2 + 10=1 + 10 = 11) (f(2)=2^2+10=4 + 10=14) Then, calculate the average rate of change: (\frac{f(2)-f(-1)}{2-(-1)}=\frac{14 - 11}{3}=\frac{3}{3}=1>0)

Step3: Calculate for option B ([-3,1])

Find (f(-3)) and (f(1)) (f(-3)=(-3)^2+10=9 + 10=19) (f(1)=1^2+10=1+10 = 11) Calculate the average rate of change: (\frac{f(1)-f(-3)}{1-(-3)}=\frac{11 - 19}{4}=\frac{-8}{4}=-2<0)

Step4: Calculate for option C ([-4,-1])

Find (f(-4)) and (f(-1)) (f(-4)=(-4)^2+10=16 + 10=26) (f(-1)=(-1)^2+10=1+10 = 11) Calculate the average rate of change: (\frac{f(-1)-f(-4)}{-1-(-4)}=\frac{11 - 26}{3}=\frac{-15}{3}=-5<0)

Step5: Calculate for option D ([-3,3])

Find (f(-3)) and (f(3)) (f(-3)=(-3)^2+10=9 + 10=19) (f(3)=3^2+10=9+10 = 19) Calculate the average rate of change: (\frac{f(3)-f(-3)}{3-(-3)}=\frac{19 - 19}{6}=0)

Answer:

A. ([-1,2])