A. Find the average rate of change of the given function on the interval [-1,3]. Enter only the
simplified numerical value without any spaces:
B. What is the geometric meaning of the average rate of change on [-1,3]? Explain what it
represents in one sentence. It represents
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UpStudy AI · Accepted Answer

1. Compute the average rate of change using the formula  
   $$
   \frac{f(3)-f(-1)}{3-(-1)}.
   $$  
   For the function $$ f(x) = x^2 $$, we have  
   $$
   f(3)=3^2=9 \quad \text{and} \quad f(-1)=(-1)^2=1.
   $$  
   Substitute these values:  
   $$
   \frac{9-1}{3+1} = \frac{8}{4} = 2.
   $$

2. It represents the slope of the secant line connecting the points $$(-1, f(-1))$$ and $$(3, f(3))$$ on the graph of the function.
1. The average rate of change is 2. 2. It represents the slope of the line connecting the points $$(-1,1)$$ and $$(3,9)$$.

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