textbook videos +\n| q | 2.4 | 2.6 | 2.8 | 3 | 3.2 |\n| h(q) | 1964 | 3049 | 4734 | 7351 | 11414 |\nestimate…
textbook videos +\n| q | 2.4 | 2.6 | 2.8 | 3 | 3.2 |\n| h(q) | 1964 | 3049 | 4734 | 7351 | 11414 |\nestimate h(2.8) using the table above.\nhint: find the average rate of change on either side of h(2.8), and then average those two values.\nh(2.8) ≈ \nquestion help: video message instructor
Answer
Explanation:
Step1: Calculate left - hand difference quotient
The left - hand difference quotient for estimating the derivative at $q = 2.8$ is $\frac{h(2.8)-h(2.6)}{2.8 - 2.6}$. Substitute $h(2.8)=4734$ and $h(2.6)=3049$ into the formula: $\frac{4734 - 3049}{2.8 - 2.6}=\frac{1685}{0.2}=8425$.
Step2: Calculate right - hand difference quotient
The right - hand difference quotient for estimating the derivative at $q = 2.8$ is $\frac{h(3)-h(2.8)}{3 - 2.8}$. Substitute $h(3)=7351$ and $h(2.8)=4734$ into the formula: $\frac{7351 - 4734}{3 - 2.8}=\frac{2617}{0.2}=13085$.
Step3: Average the two difference quotients
To estimate $h'(2.8)$, we average the left - hand and right - hand difference quotients. $h'(2.8)\approx\frac{8425 + 13085}{2}=\frac{21510}{2}=10755$.
Answer:
$10755$