Questions: a. Use the applet above to determine the value of the difference quotient (the average rate of change) near the point (2, f(2)) when:
i. the length of h is 5.
ii. the length of h is 3
iii. the length of h is 1.6
iv. the length of h is 0.5,6
v. the length of h is 0.15.
b. Determine if the following statement is true or false.
True
✓ infinity
As the value of h gets smaller and smaller, the value of the difference quotient becomes a better and better approximation function f near the point (2, f(2)).
Transcript text: a. Use the applet above to determine the value of the difference quotient (the average rate of change) near the point $(2, f(2))$ when:
i. the length of $h$ is 5 .
ii. the length of $h$ is 3
iii. the length of $h$ is 1.6
iv. the length of $h$ is $0.5,6$
v. the length of $h$ is 0.15 .
b. Determine if the following statement is true or false.
True
$\checkmark \infty$
sthe value of $h$ gets smaller and smaller, the value of the difference quotient becomes a better and better approximation function $f$ near the point $(2, f(2))$.
Solution
Solution Steps
Step 1: Identify the given point and the function
The given point is \( (2, f(2)) \). From the graph, we can see that \( f(2) = 10 \).
Step 2: Determine the value of the difference quotient for different lengths of \( h \)
The difference quotient is given by:
\[ \frac{f(2+h) - f(2)}{h} \]
Step 3: Calculate the difference quotient for \( h = 5 \)