Answer:
The option D represents an interval with a positive average rate of change.
Step-by-step explanation:
Let [tex]f(x) = x^{2}+10[/tex], the average rate of change on the interval [tex][a,b][/tex] is represented by the definition of the secant line:
[tex]\bar f = \frac{f(b) -f(a)}{b-a}[/tex] (1)
Where:
[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds, dimensionless.
[tex]f(a)[/tex], [tex]f(b)[/tex] - Function evaluated at lower and upper bounds, dimensionless.
Now we proceed to check each option:
A. [tex]a = -3[/tex], [tex]b = 3[/tex]
[tex]\bar f = \frac{19-19}{3-(-3)}[/tex]
[tex]\bar f = 0[/tex]
B. [tex]a = -4[/tex], [tex]b = -1[/tex]
[tex]\bar f = \frac{11-26}{(-1)-(-4)}[/tex]
[tex]\bar f = -5[/tex]
C. [tex]a = -3[/tex], [tex]b = 1[/tex]
[tex]\bar f = \frac{11-19}{1-(-3)}[/tex]
[tex]\bar f = -2[/tex]
D. [tex]a = -1[/tex]. [tex]b = 2[/tex]
[tex]\bar f = \frac{14-11}{2-(-1)}[/tex]
[tex]\bar f = 1[/tex]
The option D represents an interval with a positive average rate of change.
